Purpose: In this research, non-linear three dimensional finite element models with contact elements were constructed. For the investigations of the distributions of contact stresses, 3 units fixed partial dentures model were studied, especially on the interface of the gold screw and cylinder, abutment screw. Methods: 3 types of models were constructed ; the basic fixed partial denture in molar region with 3 units and 3 implants, the intermediate pontic fixed partial denture model with 3 units and 2 implants, and the extension pontic fixed partial denture model with 3 units and 2 implants. For all types, the external loading due to chewing was simulated by applying $45^{circ}$ linguo-buccal loading of 300 N to the medial crown. For the simulation of the clamping force which clinically occurs due to the torque, thermal expansion was provided to the cylinder as a preload. Results: Under 300 N concentrated loading to the medial crown, the maximum contact stress between abutment screw and gold screw was 86.85~175.86MPa without preload, while the maximum contact stress on the same area was 25.59~57.84MPa with preload. Conclusion: The preloading affected the outcomes of the finite element stress analysis. Reflecting the clinical conditions, the preloading conditions should be considered for other practical study utilizing FEA. For the study of the contact stresses and related motions, various conditions, such as frictional coefficient changes, gap between contact surfaces, were also varied and analyzed.