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Mechanical stresses occurring in electrical contact situations were calculated with the aid of the finite element method (FEM). As a first step the stresses in a gold film on a nickel substrate, indented by a sphere, were calculated, assuming elastic deformations. With the same normal contact force the stresses in the film can differ enormously for different film thicknesses of the gold. In many electrical contact situations plastic deformations occur. As a second step these deformations were also calculated. Therefore it is necessary to know the plastic part of the stress-strain curve. A method is presented for obtaining this curve for thin metal films from a Brinell indentation test. An elasticplastic contact situation for a cylinder sliding over a gold surface with different friction coefficients is investigated. It is shown that phenomena like the onset of prow formation and cracking of the surface can be observed from the calculated results.