In this paper, a set of problems related to development and numerical implementation of a mathematical model of elastic-plastic deformation of materials under intensive external disturbances is considered. A simplified thermodynamically correct model of elastically compressible plastic medium is proposed for analysis of developed flows with negligible elastic changes of particle shapes. An efficient numerical algorithm of geometrically linear model is constructed by the method of splitting by physical processes and spatial variables. Problem solution is based on finitedifference scheme of predictor-corrector type with controlled artificial dissipation of energy in accordance with the Ivanov’s method. A special correction procedure similar to the Wilkins stress correction procedure deals with irreversible deformation. Numerical algorithm validation is performed by results validation with the exact solution of a problem for plastic shock wave propagation in the unbounded medium.