Purpose. Determining a relationship between the shear/failure of the rock mass and the technogenic earthquakes caused by them during underground mining of ore deposits with the derivation of an equation for the dependence of the technogenic earthquake indicators for the conditions of the Zhezkazgan copper-ore field. Methods. The research methodology consists of studying and analyzing early research on technogenic earthquakes by the method of statistical data processing. Calculation of rock mass deformation distribution in the study area is based on numerical modeling in the Comsol Multiphysics 5.6 and MATLAB 2020 software package environment. Calculations are performed based on solving a plane problem using the Finite Element Method (FEM). Findings. Based on the transition from the failure area to subsidence and shear values of the overlying rock mass stratum, an equation for the dependence of the earthquake magnitude on the numerical values of the mass subsidence or shear has been obtained. Originality. For the first time, based on the physics and geomechanics of rock mass shear processes, empirical-analytical formulas have been obtained that make it possible to predict the technogenic earthquake magnitude during underground mining of ore deposits in the conditions of the Zhezkazgan copper-ore field. Practical implications. Preliminary predictive calculations made by the obtained formulas for the conditions of the active mine No. 31 of the East-Zhezkazgan mine, ТОО Kazakhmys Smelting, show acceptable results of magnitude value, comparable to in-situ measurements during field mining. This prediction makes it possible to pre-calculate the technogenic earthquake magnitude at the stage of designing mining operations and make appropriate scientifically sound decisions during further mining of the field.