This paper presents a stress controlled boundary slip model and predicts the fluid-solid interface slip in a system of parallel sliding plates or a sphere approaching a smooth plane. The numerical simulation results are in striking agreement with the existing experimental observations. This model assumes that there is a limiting shear stress. No slip occurs if the surface shear stress is smaller than the limiting shear stress, and slip occurs when the surface shear stress equals it. It is found that boundary slip dramatically decreases the hydrodynamic pressure if the two squeezed surfaces have the same slip property. Finally, the hydrodynamic force reaches a saturation status and almost does not decrease any more. Compared with the no-slip solution, hydrodynamic force is found to decrease by over two orders in the case of boundary slip. When the squeezed surfaces have different slip properties, however, the hydrodynamic pressure is mainly controlled by the surface having a smaller surface limiting shear stress, and reduces more slowly compared with the case of two surfaces having the same slip property. Even when one of the surfaces has a zero surface limiting shear stress, a considerable hydrodynamic force still exists.