The dynamic buckling of a cylindrical shell subject to a uniform axial compression, which is a linear function of time, is examined within the framework of small strain elasto-plasticity. The material of the shell is incompressible and the effect of the elastic unloading is not taken into consideration. Initially, employing the deformation theory, the fundamental relations and Donnell type stability equations have been obtained. Finally, by using the Galerkin's methods the closed form solutions are presented. Comparing the results with those in the literature validates the present analysis.