The locations of periodic points for Stokes flow in a rectangular cavi
ty is studied. Discontinuous and sinusoidal corotating periodic motion
s of the top and bottom walls are considered. An effective algorithm f
or one-dimensional search based on the use of symmetry conditions of t
he flow is proposed for both cases. It permits one to find and classif
y all periodic points of low-order periodicity. Specific features of t
he bifurcation diagrams are noticed. Two typical examples of Row with
the dye blob situated around an elliptic or a hyperbolic periodic poin
t show a striking difference in mixing properties.