Abstract. One of the most important problems in the design of press-and shrink-fitted assemblies is to avoid stress concentrations at the contact of two bodies. A method is presented whereby the contact-stresses can be made uniform by using variable interferences. In the proposed method the finite element technique is applied to determine the stresses of composite bodies, ignoring the effects of friction at the contact surfaces. A method of optimum structural design is used to obtain a uniform contact stress within the limit of the contraction force. In this method, interferences at contact nodal points are used as design variables. Some simple examples are presented and the effectiveness of the proposed approach is also demonstrated. ement methods. Some numerically controlled machines have been developed which can produce any shape of the component with great accuracy. Thus, the opportunity to consider variable interference allowances for composite bodies is available.Considering these points, the authors propose a method for determining the uniform stress distribution between contact surfaces of composite bodies with variable interferences, by using the finite element method. Some example problems are solved analytically for uniform tangential or normal stress at the contact surfaces. The results of the uniform stresses demonstrate the efficiency of the method.