In the article, within the framework of the dynamic theory of elasticity, a mathematical model of the impact of seismic blast waves on rock mass is presented, including a working. The increase in the volume of mining operations in complex mining and geological conditions, taking into account the influence of the explosion energy, is closely connected with the analysis of the main parameters of the stress-strain state of the rock massif including a working. The latter leads to the need to determine the safe parameters of drilling and blasting operations that ensure the operational state of mining. The main danger in detonation of an explosive charge near an active working is a seismic explosive wave which characteristics are determined by the properties of soil and parameters of drilling and blasting operations. The determination of stress fields and displacement velocities in rock mass requires the use of a modern mathematical apparatus for its solution. For numerical solution of the given boundary value problem by the method of finite differences, an original calculation-difference scheme is constructed. The application of the splitting method for solving a two-dimensional boundary value problem is reduced to the solution of spatially one-dimensional differential equations. For the obtained numerical algorithm, an effective computational software has been developed. Numerical solutions of the model problem are given for the case when the shape of the working has a form of an ellipse.