It is well known that in engineering practice high stresses occur and that these stresses depend on the shapes and the loads of the bodies in unilateral contact. The stress distribution is often not smooth and has some singularities, thereby decreasing the lifetime of the machine elements. It is an important objective to obtain a smooth stress distribution when optimizing the shape of the elements. One of the goals of this paper is to present a method that resolves the above problem. By controlling the contact pressure a prescribed, smooth contact-pressure distribution can be achieved. The optimization problems take into account the limit stress constraints of the material. In the present paper two types of contact problems are investigated. Firstly, contact optimization problems are analyzed assuming linear elasticity and small displacements, including steady-state wear process. Two numerical examples are presented on this topic for a rolling machine element: a punch optimization and a shape optimization. We also investigated which parameter values of the controlling function result in the maximum loadability. This can be useful in the design of brakes or bearings. In the second part of the paper the solution of the contact problem for large displacements and deformations is investigated where an air-spring is analyzed by calculating the nonlinear load-displacement curve and comparing it with measurements. © 2007 Journal of Mechanical Engineering. All rights reserved.