This paper presents a fast and robust three-dimensional contact computation tool taking into account the effect of cyclic wear induced from fretting solicitations under the gross slip regime. The wear prediction is established on a friction-dissipated energy criteria. The material response is assumed elastic. The contact solver is based on the half-space assumption and the algorithm core is similar to the one originally proposed by Kalker (1990, Three Dimensional Elastic Bodies in Rolling Contact, Kluwer, Dordrecht) for normal loading. In the numerical procedure the center of pressure may be imposed. The effect of surface shear stress is considered through a Coulomb friction coefficient. The conjugate gradient scheme presented by Polonsky and Keer (1999, Wear, 231, pp. 206–219) and an improved fast Fourier transform (FFT) acceleration technique similar to the one developed by Liu (2000, Wear, 243, pp. 101–111) are used. Results for elementary geometries in the gross slip regime are presented. It is shown that the surface geometry influences the contact pressure and surface shear stress distributions found after each loading cycle. It is also shown that wear tends to be uniformly distributed. This process continuously modifies the micro- and macrogeometry of the rubbing surfaces, leading after a given number of cycles to (i) an optimum or ideal contact geometry and (ii) a prediction of wear.