The paper discusses nonlinear axisymmetric vibrations of elastic-plastic cylindrical shells. The shell is compressed initially by an axial load and then fixed in its compressed position. After that a short-pulse or periodical lateral load is applied. The problem in question is solved by the Galerkin's method. An algorithm, which allows to get solutions for an arbitrary number of degrees of freedom, is proposed. Numerical examples are given and the possibility of chaotic vibrations is discussed. Copyright (C) 1996 Elsevier Science Ltd.