A finite element simulation of frictional contact problem between two deformable three-dimensional bodies is presented. While most aspects of this simulation have been adopted from literature, those related to the analysis of contact itself have been modified and constitute the main contribution of this work. Contact boundaries are decomposed into quadrilateral surface segments, and a new contact searching algorithm is proposed based on a node-to-segment model. Kinematics and force distribution in the contact zone are modified accordingly. A regularized friction law is employed. The approach is applicable to a wide range of contact problems, even though the presentation of numerical results is mainly related to the press fit connection problem. In this context, the numerical analysis presented provides an estimate of the force needed to create the press fit connection and gives an assessment of the deformation and stress levels for both bodies involved.