Granular shear flows in a bounded Couette geometry are studied using a two-dimensional discrete element computer simulation. Upper and lower bounding walls are flat and frictional and move in opposing directions, while the right and left boundaries are periodic. Mono-size flows of various concentrations are examined as well as flows of binary mixtures with diameter ratios of 2, 5, and 10. Mixture solid fraction ratios of small to large particles range from 0.4 to 5, with a constant overall solid fraction of 0.75 in two dimensions. Normal and shear stresses on the bounding walls are calculated for various flow conditions. Both normal and shear stresses increase with solid fraction in same-size flows, and show a dependence on the wall spacing at low concentrations. Stresses in mixture flows with low solid fraction ratios of small to large particles are higher than for the mono-size system. For a fixed overall solid fraction of 0.75, mixture flow stresses also increase with diameter ratio of large to small particles. The ratio of shear to normal stress decreases with solid fraction in same-size flows. For mixture flows with constant overall solid fraction, the ratio increases with solid fraction ratio for size ratios of five and ten; it remains relatively constant in flows with a size ratio of only two.