Purpose of the study is in reasoning of the parameters of support system, taking into account the regularity of changes in the stress-strain state of the surrounding rocks to ensure the stability of the rock massif. The first section analyzes the state of the problem and identifies ways of its scientific and practical solution. It is researched the ways of studying the mechanical properties of minerals and rocks by simulation methods. Field and laboratory methods for determining mechanical properties of rocks and numerical simulation methods are analyzed. In the second section it is made a choice of slightly metamorphic rocks investigation method and the construction of the research method. The main features of the finite element method (FEM) are viewed and the choice of the program for investigation is substantiated. Selected initial and boundary conditions in accordance with the mining and geological conditions of PJSC "DTEK Pavlogradvugillya" PSD "Dniprovska" mine. General information about the company under the terms of which the research was conducted is provided. By the means of 3D-simulation program “SolidWorks”, several variants of stress-strain state of the massif with different types of the working support are constructed. After simulation of the processes of working loads, the analysis and conclusions of the rock massif stress-strain state are made. In the third section it is viewed the recommendations for providing of the working support stability. The choice of the working support system for computer simulation is based. An analysis of the support structures used for the mining and geological conditions of Western Donbass is carried out. Recommendations of support parameters for the conditions of PJSC "DTEK Pavlogradvugillya" PSD "Dniprovska" mine and substantiation of the resource saving at the supporting of development drift were made. In the section "Labor safety" defines the measures for fire prevention and measures for the safe installation of rock bolts, the calculation of dust from the return ventilation air and protection activities. In the economic section, the indices that indicate the economic attractiveness of the decision, are viewed.