Whereas it is rather obvious that the problem of stability and post yield behaviour of a structure can be treated properly only within framework of the geometrically non-linear theory, the question arises, whether the second order effects, usually neglected when formulating the constitutive relations, play also substantial role.

Therefore, such effects as influence of various definitions of perfectly plastic material /associated with the different objective stress rates/ on the post yield behaviour of the shells is considered in the paper.

The material incompressibility, observed when plastic deformations take place, is also taken into account when formulating geometrical relations.

The results are compared with the known solutions obtained under the assumption of constant shell thickness.
The problem considered is illustrated by examples of cylindrical shells subject to the end axial forces and uniformly distributed lateral dead load.