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This paper describes the numerical method for the solution to the problem of propagation of dynamic waves in elastic media--the bicharacteristics method with the usage of the ideas of the splitting method. The bicharacteristics method is one of the most convenient methods for software creating. In this research paper we have worked on the solution for non-stationary problem of the homogeneous isotropic elastic body dynamics using the bicharacteristics method, based on which the "ProgWave" software was designed. With this software, we have obtained the plots of isolines of normal and tangent tensions, which are very important for the studies of non-stationary dynamic waves propagation in flat elastic bodies, in engineering practice at construction designs calculation, in problems of mechanical engineering, etc. [ABSTRACT FROM AUTHOR]