The goal of this study is to enhance the method for predicting geomechanical processes during mine working construction in an elastoplastic rock mass with dilatancy. We present the results of experimental research into the volumetric strength of rocks and the specifics of volumetric strain development under plastic shear. We demonstrate rock dilatancy and provide diagrams showing how volumetric plastic shear strains change at different levels of accumulated shear strains. We process the rock testing results using A.N.Stavrogin’s plasticity condition. We propose a new analytical solution for predicting the stress-strain state of the rock mass in areas with inelastic strains, based on A.N.Stavrogin’s plasticity condition. This includes equations for modelling the limit state zone of rock around a mine working. We introduce an algorithm for predicting the stress-strain state of the rock mass. We investigate how the size of the limit state zone around a mine working relates to rock dilatancy parameters, lateral stress coefficient, and working depth. We examine how contour displacements develop for a circular mine working under plane strain conditions, considering various plasticity parameters and rock dilatancy indicators. We implement A.N.Stavrogin’s plasticity condition in the Abaqus software package. Our research results help define the scope of the analytical solution. The solution remains physically meaningful only when the limit state zone forms around the entire perimeter of the mine working. The proposed numerical approach removes this limitation. It applies to any geomechanical state of the rock mass and to mine workings with any cross-sectional shape.