The issues of assessing the stability and fastening of horizontal and vertical mine workings, considering various mining and geological conditions, are relevant. The study of scientific papers related to this problem has shown that a fairly large number of works are devoted to developing methods for calculating and applying anchor-sprayed concrete support for the walls of horizontal mine workings. At the same time, there is no design model for using such a support for the trunks of vertical mine workings. In the proposed work, the method proposed in the previous work of the authors [1] is used to calculate the parameters of the anchor support of the trunks of vertical workings. To develop a methodology for calculating the thickness of the sprayed concrete coating, a model of a quadrangular plate was adopted, and methods of the theory of elasticity were applied, similar to the problem of calculating boiler walls reinforced with anchor bolts, first solved by academician A.S.Leibenzon. As a result, a new formula for determining the thickness of sprayed concrete for vertical shafts is proposed, taking into account the steps of installing anchors horizontally and vertically and the influence of the lateral rebound coefficient under the action of a gravitational stress field. The problem of determining the strength limit of anchors on a slice interacting with a sprayed concrete coating is solved. An expression is obtained for determining the minimum value of the shear stress for the applied anchors at depth in rocks with a density; a formula is derived that allows determining the upper limit of permissible distances between anchor belts vertically, different from previously known similar formulas in that it takes into account the effects of the radius of the zone of destroyed rocks, the thickness of the sprayed concrete and the ultimate strength of the sprayed concrete. In addition, in its structure, there is a factor of the angle of inclination to the horizon of the most dangerous sliding plane. Based on the results obtained, it can be concluded that a technique has been developed that allows the calculation of a combined anchor-sprayed concrete support for small vertical shafts, optimize the values of the parameters of such support and create a corresponding mathematical model.