The use of interference-fitted assemblies is very common in engineering practice, for example, in bolted connections and fitting of sleeves into cylindrical shafts. For practical-purposes, it is important to prevent stress concentrations which are generated at contact surfaces of the components assembled with interference fits. In this paper, a method for determining the interferences to uniform stress distribution at the contact boundary of the components is proposed. The finite-element method is used to solve stress and displacements in two component systems in contact with each other in which slip does not occur. The difference between maximum and minimum stresses at the contact boundary is minimized under a constraint of contact pressures, as nodal interferences are taken as design variables. The proposed method is applied to two basic examples of a rectangular plate fitted with a circular plate and a column fitted with a sleeve, to show its effectiveness.