A new method for the design of support of deep multiple non-circular workings located in tectonic areas, is presented. The method is based on a new analytical solution of the 2D problem of elasticity theory for a linearly deformable medium simulating the rock mass, weakened by an arbitrary number of arbitrarily located openings of different shapes, supported by rings from the other materials simulating the workings support. The action of tectonic forces is simulated by initial stresses in the medium the principal axes of which are inclined under an arbitrary angle with respect to the horizontal and the vertical. The corresponding software has been developed. Examples of the design are given.