A mathematical model for the hydrodynamic lubrication of finite slider bearings with velocity slip and couple stress lubricants is presented. A numerical solution for the mathematical model using finite element scheme is obtained using four node linearly interpolated quadrilateral elements. Stiffness integrals obtained from the weak form of the governing equations were solved using Gauss Quadrature to obtain a finite number of stiffness matrices. The global system of equations was obtained for the bearing and solved using Gauss Seidel iterative scheme. The converged pressure solution was used to obtain the load capacity of the bearing. Numerical experiments reveal the existence of an optimum velocity slip for which maximum benefit is obtained for the slider bearing in terms of bearing load. Increase in the slip parameter beyond this optimum value was shown not to augment the bearing load. Computations put forth also affirm that the bearing load is augmented with increase in couple stress parameter. An optimal film thickness ratio was also obtained for which load capacity is maximized with or without the application of slip to the bearing surfaces.