This is the peer reviewed version of the following article: Medková Dagmar, Ptashnyk Mariya, and Varnhorn Werner (2014), Integral representation of a solution to the Stokes–Darcy problem, Math. Meth. Appl. Sci., doi: 10.1002/mma.3330, which has been published in final form at http://dx.doi.org/10.1002/mma.3330. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.