The contact stress distribution is frequently not regular. It may contain singularities reducing the lifetime of machine elements. In order to eliminate such stress singularities, the application of contact pressure control is recommended in the contact conditions. In the paper, several classes of optimization problems are formulated for stationary and sliding contacts. Further, they are illustrated by specific examples. The relation to wear process is made as a natural way to attain the steady state contact profile satisfying the optimality conditions corresponding to minimization of the wear dissipation rate. It is assumed that the displacements and strains are small and the materials of the contacting bodies are elastic.