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Abstract. The paper addresses the problem of plastic deformation of circular membranes and shallow axisymmetric membrane shells under high-intensity loading considering rotary inertia. The resolving equations systems are obtained, the numerical implementation program and algorithms are developed. The research methods used in the paper include finite difference method, differential-incremental method of the second and fourth orders of accuracy, the Fourier series solutions with Bessel functions. The results are obtained confirming reasonability of considering rotary inertia.