Purpose. To develop analytical model for a support-enclosing rock interaction to determine parameters for operational stability of deep mine workings while decreasing metal consumption and increasing efficient use of resources. Methods.Involving various strength degradation functions and variations of physical and mechanical properties of rocks, mathematical modeling is used to consider the ranges of force action of a support on the enclosing rock mass of deep mine workings.Findings. Analytical dependence of a support effect on the rock border displacement as well as on the changes in cross section of the mine working has been obtained. Effective interval of the support force resistance to block limit zones of the rock mass deformations has been substantiated. Innovative approach relying on the priority of the support working capacity as well as its forming characteristics has been proposed. The results of the studies help regulate the use of available supports, and the development of new designs meeting the increased geomechanical requirements of deep mining. Practical implications.The results of the studies help regulate the use of available supports, and the development of new designs meeting the increased geomechanical requirements of deep mining and to determine the required parameters of both force and deformational characteristics of supports making.

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