A simple shear flow of binary granular mixtures is numerically simulated. In many respects the numerical schemes employed here are similar to those originally used in molecular dynamics simulations and also to those used in a series of Campbell's simulations of granular flows. However, the averaging method has been extended to suit for bimodal flow calculations. Flows are rather dense and collisions are assumed to be the dominant mechanism for stress generation. It has been found that the contribution to the collisional shear stress from the collisions between small particles is rather insignificant except near the boundaries. It has been also found that for a given initial system's solid volume fraction the total collisional shear stress tends to increase as the difference in size decreases.