  In this paper, all the known classical solutions of plane perfect plasticity
system under Saint Venant -- Tresca -- von Mises yield criterion are associated
with some group of point symmetries. The equations of slip-line families for
all solutions are constructed, which permits to determine explicitly boundaries
of plastic areas.
  It is shown, how one can determine the compatible velocity solution for known
stresses, considering symmetries. Some invariant solutions of velocities for
Prandtl stresses are constructed. The mechanical sense of obtained velocity
fields is discussed.
