<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2025 Workiva-->
<!--r:2a58e851-be17-466f-b18f-17902d8b7772,g:c6e7cda1-2668-4ab8-b572-eb2bb4d043a8-->
<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:roleRef roleURI="http://www.westpharma.com/role/Cover" xlink:type="simple" xlink:href="wst-20251023.xsd#Cover"/>
  <link:presentationLink xlink:role="http://www.westpharma.com/role/Cover" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:href="wst-20251023.xsd#wst_DocumentAndEntityInformationAbstract"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey_b711e897-6567-4f8d-972d-744080d3446c" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey"/>
    <link:presentationArc order="1" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_EntityCentralIndexKey_b711e897-6567-4f8d-972d-744080d3446c" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType_5b141586-8bfd-4cfd-89a5-5799c0604429" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentType"/>
    <link:presentationArc order="2" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_DocumentType_5b141586-8bfd-4cfd-89a5-5799c0604429" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate_512261a3-bc77-4c99-bda1-ca0bb6bd289e" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentPeriodEndDate"/>
    <link:presentationArc order="3" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_DocumentPeriodEndDate_512261a3-bc77-4c99-bda1-ca0bb6bd289e" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName_5d4589de-34af-4a41-b74e-a53838233529" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityRegistrantName"/>
    <link:presentationArc order="4" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_EntityRegistrantName_5d4589de-34af-4a41-b74e-a53838233529" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode_f5b08d23-995d-4c43-91ef-a0e209070e20" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:presentationArc order="5" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_EntityIncorporationStateCountryCode_f5b08d23-995d-4c43-91ef-a0e209070e20" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber_ecb2ac9e-75f8-40d9-8c0b-2a8a169791c2" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityFileNumber"/>
    <link:presentationArc order="6" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_EntityFileNumber_ecb2ac9e-75f8-40d9-8c0b-2a8a169791c2" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber_f01bbab5-58d7-4b35-8486-334baac01cba" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:presentationArc order="7" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_EntityTaxIdentificationNumber_f01bbab5-58d7-4b35-8486-334baac01cba" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1_6e565c61-9b0f-4a0c-992f-a619caae1929" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressAddressLine1"/>
    <link:presentationArc order="8" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_EntityAddressAddressLine1_6e565c61-9b0f-4a0c-992f-a619caae1929" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown_24744699-93ab-4ae9-bd85-d6e09db9d336" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressCityOrTown"/>
    <link:presentationArc order="9" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_EntityAddressCityOrTown_24744699-93ab-4ae9-bd85-d6e09db9d336" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince_bc5e57ca-f1c4-4d53-be55-8b8044e19a11" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressStateOrProvince"/>
    <link:presentationArc order="10" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_EntityAddressStateOrProvince_bc5e57ca-f1c4-4d53-be55-8b8044e19a11" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode_d7ade881-9f39-40fa-95ad-34bd5a003a1a" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressPostalZipCode"/>
    <link:presentationArc order="11" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_EntityAddressPostalZipCode_d7ade881-9f39-40fa-95ad-34bd5a003a1a" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode_18aa2722-3122-4778-a7bd-edd28dd964a4" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CityAreaCode"/>
    <link:presentationArc order="12" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_CityAreaCode_18aa2722-3122-4778-a7bd-edd28dd964a4" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber_e94e91ef-1438-4445-a0a0-d8a92943e5f0" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LocalPhoneNumber"/>
    <link:presentationArc order="13" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_LocalPhoneNumber_e94e91ef-1438-4445-a0a0-d8a92943e5f0" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_WrittenCommunications_300128df-9201-431a-b508-e0990c5fce11" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_WrittenCommunications"/>
    <link:presentationArc order="14" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_WrittenCommunications_300128df-9201-431a-b508-e0990c5fce11" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SolicitingMaterial_1f49b728-f67e-40ac-afa3-04368b1104b2" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_SolicitingMaterial"/>
    <link:presentationArc order="15" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_SolicitingMaterial_1f49b728-f67e-40ac-afa3-04368b1104b2" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementTenderOffer_7a1fe0e1-4930-45b4-8966-ad284ba85a89" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_PreCommencementTenderOffer"/>
    <link:presentationArc order="16" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_PreCommencementTenderOffer_7a1fe0e1-4930-45b4-8966-ad284ba85a89" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementIssuerTenderOffer_f7168ac0-d646-4c5a-8bff-6c87d2ffc586" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_PreCommencementIssuerTenderOffer"/>
    <link:presentationArc order="17" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_PreCommencementIssuerTenderOffer_f7168ac0-d646-4c5a-8bff-6c87d2ffc586" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle_38edcd37-ad3f-4af3-bc7e-e056ac2f2743" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_Security12bTitle"/>
    <link:presentationArc order="18" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_Security12bTitle_38edcd37-ad3f-4af3-bc7e-e056ac2f2743" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol_8872df6e-4158-4274-97b7-4e2154acf859" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_TradingSymbol"/>
    <link:presentationArc order="19" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_TradingSymbol_8872df6e-4158-4274-97b7-4e2154acf859" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName_fb51a65c-fe7c-4263-b433-2703fdee91b4" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_SecurityExchangeName"/>
    <link:presentationArc order="20" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_SecurityExchangeName_fb51a65c-fe7c-4263-b433-2703fdee91b4" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany_a5308334-d301-4c0c-92ca-9b6c0d922413" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:presentationArc order="21" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_EntityEmergingGrowthCompany_a5308334-d301-4c0c-92ca-9b6c0d922413" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag_41f96f96-2c8f-469c-918f-6ba8d34f1043" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AmendmentFlag"/>
    <link:presentationArc order="22" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_wst_DocumentAndEntityInformationAbstract_bf4b36d4-e1c3-4f34-83f7-f5c836cd797f" xlink:to="loc_dei_AmendmentFlag_41f96f96-2c8f-469c-918f-6ba8d34f1043" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
  </link:presentationLink>
</link:linkbase>
