Contact problems with friction or heat generation appear in many different fields of mechanical engineering. The paper is concerned with the analysis as well as the numerical solution of the topology optimization problems for elasto–plastic rather than elastic structures in unilateral frictional contact with a rigid foundation. The small strain plasticity model with linear hardening and a von Mises effective stress is used. The displacement and stress of this structure in contact are governed by the system of the coupled variational inequalities. The material density function is design variable. The topology optimization problem consists in finding such material distribution of the domain occupied by the body in contact to minimize the contact stress and to ensure the uniform distribution of this stress. Using the regularization of the stress projection operator on the set of admissible generalized stresses as well as of the friction functional this original structural optimization problem is replaced by the regularized one. The phase field approach is used to approximate sharp interface problem formulation and to calculate the derivative of the cost functional. The relation between sharp interface and phase field optimization problems is investigated. The cost functional derivative is calculated. The Lagrange multiplier technique is used to formulate the set of necessary optimality conditions. Gradient flow approach in the form of modified Cahn-Hilliard boundary value problem is used to evaluate optimal topology domain. Mixed finite element formulation of modified Cahn-Hilliard problem is used. The evolution of the structure topology is governed by the cost functional derivative. The examples of minimal contact stress topologies are provided and discussed.