Fourier series expansion and finite element method are used to determine the contact pressure distribution at the mating surfaces between two members assembled together with an initial interference fit. The approach to the solution of the problem involves setting up a Fourier series expansion which represents the contact pressure distribution at the nodal points on the mating surfaces between the two members. The finite element method is then used to determine the resulting displacements. Results are obtained for the case of a hollow shaft pressed into a bearing inner ring and a bearing outer ring pressed into a housing. The effect of different materials used on combination for the bearing rings, shaft, and housing is investigated.