A numerical investigation was carried out to study the mixing behavior of Stokes flows in a rectangular cavity stirred by three square rods. The square loops of the rods move in such a way that a pseudo-Anosov map can be built in the flow domain in the augmented phase space. The finite volume method was used, and the flow domain was meshed by staggered grids with the periodic boundary conditions of the rod motion being imposed by the mesh supposition technique. Fluid particle tracking was carried out by a fourth-order Runge–Kutta scheme. Tracer stretches from different initial positions were used to evaluate interface prediction by a pseudo-Anosov map. The colored short period Poincaré section was obtained to reveal the size of the domain in which the pseudo-Anosov map was in effect. Dye advection patterns were used to analyze chaotic advection of passive tracer particles using statistical concepts such as “variances” and “complete spatial randomness.” For the fluid in the core region of the cavity, tracer interface stretches experienced exponential increases and had the same power index as that predicted by the pseudo-Anosov map matrix.