Abstract
Second mining of the earlier abandont deposits at the operating mines is one of the urgent scientific-technical problems. The principal components of this problem are questions of reliability of underground structures for preserving of the earth surface and attaining the high level of safety of mining operatios. The report describes mathematical models for evaluation and control of reliability of underground structures enabling forecasting of the probability of caving of overlying rock strata and pillar failure during second underground mining. Theoretical propositions is the basis for creation of computer-aided control systems for geomechanical processes in mines.