Numerical investigation was conducted to study the mixing behavior of Stokes flows in a rectangular cavity stirred by alternating motion of three square rods. The square loops of rod moved in two different ways that a Pseudo-Anosov map could be built in the flow domain in the augmented phase space. The finite volume method was used to solve the flow field with the periodic boundary conditions of the rod motion being imposed by the mesh supposition technique. The flow domain was meshed by staggered grids and the discretization schemes for control equations were accurate to the second-order resulting from the use of central differencing. Fluid particle tracking was conducted by a fourth-order Runge-Kutta scheme. The Poincaré section was obtained to reveal the size of the domain in which the Pseudo-Anosov map almost covered the whole cavity region except for four corner zones. The evolution patterns of tracers from different initial positions were computed to characterize the mixing process.Tracer interface stretches experienced exponential increases and had the larger power index than that predicted by the Pseudo-Anosov（pA）map matrix，which was due to the local secondary folding caused by the details of flow field

such as shapes of rods

rod trajectories and so on.