Summary: We formulate two problems of optimal design for mechanical structures in unilateral contact: the truss topology problem and the material design problem for elastic bodies. In both cases we consider general multi-load formulations, where for each loading case we may have different set of contact constraints (rigid obstacles). We show that both problems (after discretization of the latter one) can be rewritten as mathematical programs, which only differ in the character of the input data but otherwise have identical structure and thus allow the same algorithmic approach. We propose an iterative optimization algorithm based on penalty-barrier methods. A series of numerical examples demonstrates the efficiency of our approach.