In this paper, the influence of surface roughness on the local tribological load with a dry sliding contact is studied. First, three artificial rough surfaces with similar structure but different asperity heights are generated and projected on a smooth ball. After that, a contact pattern is determined between a rough ball and a smooth surface taking into account the elastic only as well as the linear elastic-perfectly plastic material description. On the basis of the calculated contact pressure distribution, the subsurface stresses and a three-dimensional temperature distribution in the sliding contact are calculated. The solutions show that a low surface roughness not necessarily results in low local tribological load of the surface.