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Here we consider a class of shape optimization problems constrained by nonlocal equations which involve interface\u2013dependent kernels. We derive a novel shape derivative associated to the nonlocal system model and solve the problem by established numerical techniques. The code for obtaining the results in this paper is published at (<jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"uri\" xlink:href=\"https:\/\/github.com\/schustermatthias\/nlshape\">https:\/\/github.com\/schustermatthias\/nlshape<\/jats:ext-link>).<\/jats:p>","DOI":"10.1007\/s10589-024-00575-7","type":"journal-article","created":{"date-parts":[[2024,5,7]],"date-time":"2024-05-07T19:01:36Z","timestamp":1715108496000},"page":"963-997","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Shape optimization for interface identification in nonlocal models"],"prefix":"10.1007","volume":"88","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9355-1076","authenticated-orcid":false,"given":"Matthias","family":"Schuster","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0351-0044","authenticated-orcid":false,"given":"Christian","family":"Vollmann","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7665-130X","authenticated-orcid":false,"given":"Volker","family":"Schulz","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,5,7]]},"reference":[{"key":"575_CR1","volume-title":"Automated Solution of Differential Equations by the Finite Element Method","author":"K-A Mardal","year":"2012","unstructured":"Mardal, K.-A., Logg, A., Wells, G.N., et al.: Automated Solution of Differential Equations by the Finite Element Method. 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