In this paper, the pressure distribution and load capacity of an infinitely wide exponentially shaped slider bearing lubricated with a non Newtonian couple stress fluid is presented. Based on Stokes micro continuum theory, the effect of couple stresses on the pressure distribution and load are computed using continuous Galerkin finite element method. The domain is discretized into uniform mesh of quadratic isoparametric elements and Gauss quadrature used to numerically integrate the stiffness integrals to obtain stiffness matrices for all elements which are subsequently assembled to form the global system of equations. The resulting global matrix is solved using Gauss Seidel iterative scheme. The numerical method adopted for the solution is shown to produce convergent results when implemented on a sequence of successively finer meshes. Having established the reliability of the numerical method, parametric studies are carried out to show the effects of couple stresses and aspect ratio on the pressure distribution and load. Computations put forward show that the effect of couple stresses is to enhance the load carrying capacity of the bearing. It has also been shown that compared to the Newtonian case, the pressure developed in the clearance zone of the bearing is augmented.