The paper presents a numerical model to investigate fretting wear either under partial or gross slip conditions. An efficient three-dimensional elastic–static contact model to solve both the normal contact problem and the tangential contact problem is presented. The contact model is validated with analytical solutions for a sphere on flat geometry. A wear law issued from the literature and based on the friction energy is used to simulate surface wear. Numerical friction logs are obtained and the wear rate evolution is found to be highly dependent on the tangential displacement.