The article presents a physical and mathematical model of the propagation of air shock waves in the network of coal mine workings after an instant explosion of the methane-air mixture in a given area. An approach to the implementation of a method for solving problems on the propagation of air shock waves in a branched network of mine workings is presented, taking into account arbitrary angles of their conjugation. The results of calculating the propagation of air shock waves in the model networks of mine workings are presented.