Although many wear criteria have been proposed, none is intrinsic to the materials and to the structures in contact. We propose new computational methods for modelling the wear phenomenon and to improve the meaning of these criteria. To interpret sliding wear experiments, numerical calculations have been performed to estimate the mechanical state in the vicinity of the wear region and to infer the dissipation mechanism activated. Calculations in two and three dimensions are proposed to estimate the stress, and the total and plastic strain cycles near the contact under repeated loadings. A result is the stress and strain amplitudes which are derived for different hertzian loadings based on measured friction coefficients. To evaluate wear and fatigue properties, plastic strain amplitude and dissipation rate are also estimated. The modification induced by wear of the original contact geometry is accounted for following the proposals of Kapoor and Johnson (J. Mech. Phys., Solids, 34 (3) (1992) 223–239). The initial contact geometry (circular) is modified by wear so that the contact surface increases and the contact stress decreases. To account for these effects, computations are made with different geometries and hertzian pressure varying from initial conditions to the stabilized state corresponding to shakedown conditions. The plastic strain amplitude and the rachetting rate evolution are then obtained.