Numerical simulation is performed for steady state flows in a driven cavity at low Reynolds numbers. The flows of incompressible viscous fluid are driven by the top lid of a cubic cavity which slides at constant speed in directions not parallel to the sidewalls. The Reynolds number Re and the angle of lid motion θ are adopted as the governing parameters. Structure of streamlines is studied by means of the Poincare map and the rotation number N of the tori formed by streamlines.The rotation number N of the tori is given as a function of (Re, θ). The appropriateness of using N as an index of mixing efficiency is discussed.