In this study a continuous asymptotic model is developed to describe the rigid-perfectly plastic deformation of a single rough surface in contact with an ideally smooth and rigid counter-surface. The geometry of the rough surface is assumed to be fractal, and is modeled by an effective fractal surface compressed into the ideally smooth and rigid counter-surface. The rough self-affine fractal structure of the effective surface is approximated using a deterministic Cantor set representation. The proposed model admits an analytic solution incorporating volume conservation. Presented results illustrate the effects of volume conservation and initial surface roughness on the rigid-perfectly plastic deformation that occurs during contact processes. The results from this model are compared with existing experimental load displacement results for the deformation of a ground steel surface.