Abstract: Finite length contact problems widely exist in gear transmission and roller bearings, and the stress concentration at the two ends of the rollers significantly affects the fatigue life of mechanical elements. This paper presented a numerical model to simulate the contact behaviors of finite line contact. The numerical model is based on the matrix formulation and overlapping concept. The solution of the model is then obtained with conjugate gradient method and the fast Fourier transform. Furthermore, this approach is extended to investigate the influences of the free edges and tangential force on stick slip in the contact zone. The results demonstrate that when the two rollers in contact are under the coincident end condition, the stick zone shrink at the free ends. Moreover, the increase of tangential force enhances the shear traction in the slip region nearby the two free edges.