The paper deals with the problem of stability of rigid-perfectly plastic shells at the yield point load.

The material incompressibility, observed when plastic deformations take place, is taken into account and the results are compared with the known solution obtained when the thickness of the shell is assumed to be constant.

The influence of different definitions of a perfectly plastic material on the post yield behaviour of the shells is also considered. The question is illustrated by the examples of cylindrical shells subject to axial end forces and uniformly distributed lateral dead load.