A numerical investigation of a viscous incompressible fluid confined in a closed circular cylindrical container is made. The top and side wall are in rotation with a constant angular velocity, and the bottom is held fixed. A numerical scheme using the full Navier-Stokes equations is developed. For small or moderate Reynolds numbers (Re = ΩL2 /ν), the convergence of iteration is quite rapid. When the Reynolds number increases, the flow in the bottom boundary layer and the viscous core is intensified. An initial value problem is also investigated for Re = 1000 and 5000. The flow development of the bottom boundary layer and the viscous core is clearly exhibited. Some experimental investigation is also made. The numerical solution agrees very well with the analytic solution for small Reynolds numbers and with the experimental observation for moderate and high Reynolds numbers.