This paper presents a finite element calculation of frictionless, non-adhesive, contact between a rigid plane and an clasto-plastic solid with a self-affine fractal surface. The calculations are conducted within an explicit dynamic Lagrangian framework. The elastoplastic response of the material is described by a J(2) isotropic plasticity law. Parametric studies are used to establish general relations between contact properties and key material parameters. In all cases, the contact area A rises linearly with the applied load. The rate of increase grows as the yield stress sigma(y) decreases, scaling as a power of sigma(y) over the range typical of real materials. Results for A from different plasticity laws and surface morphologies can all be described by a simple scaling formula. Plasticity produces qualitative changes in the distributions of local pressures in the contact and of the size of connected contact regions. The probability of large local pressures is decreased, while large clusters become more likely. Loading-unloading cycles are considered and the total plastic work is found to be nearly constant over a wide range of yield stresses. (c) 2005 Elsevier Ltd. All rights reserved.