Numerical studies of three-dimensional flows in a cubical container with a stable vertical temperature stratification are carried out. Flows are driven by the top Iid, which slides in its own plane at a constant speed. The top wall is maintained at a higher temperature than the bottom wall. The end walls and the side walls are thermally insulated. Numerical solutions are obtained over a wide range of physical parameters, i.e. 10(2) less than or equal to Re less than or equal to 2 x 10(3), 0 less than or equal to Ri less than or equal to 10.0 and Pr = 0.71, where the mixed,convection parameter Ri = Gr . Re-2. Systematical comparison of the three-dimensional numerical solutions with the previously reported two-dimensional results illuminates the impact of thermal stratification on the three-dimensional flow characteristics. When Ri " 0(1), the effect of the vertical temperature gradient is minor, and the flow structures are similar to those of the non-stratified fluid flows in a conventional lid-driven cavity flow. Fluids in the primary vortex are well mixed, and the temperature is fairly uniform in the main circulating region. When Ri greater than or equal to 0(1), the stable temperature distribution tends to suppress the vertical fluid motion. Much of the fluid motion takes place in the vicinity of the top sliding lid and the bulk of the cavity region is nearly stagnant. When Ri " 0(1), the fluid motion exhibits vertically layered vortex structures. The Nusselt number is computed at the top and bottom wall, and this also illustrates the varying flow characteristics as Ri encompasses a broad range. Extensive numerical flow visualizations are conducted. Plots demonstrating the primary hows in the (x-y) plane and the secondary flows in the (y-z) plane are presented. These display the influences of Re and Ri on the basic character of the flow and the three-dimensional effects.