Abstract: With the increasing social attention on mining induced subsidence and eco-environmental problems,it is imperative to carry out sustainable mining.Facing the new situation,we need to conduct more systematic and in-depth research based on the current research results.In this paper,the rock strata movement theories at home and abroad,their advantages and disadvantages and their application conditions were systematically reviewed when the goaf was controlled by caving method and backfill method.The important role of key strata theory in the theories of rock strata movement and surface subsidence was highlighted.Based on mining induced rock mechanics,the changes of main roof’s fracture location and length were analyzed.The model considers that the focus of hyperbola is located on the main key stratum.The hyperbola model integrates the masonry beam theory and the surface subsidence theory organically through key strata theory.In addition,the model describes the overall movement law of the overlying strata in the coal seam.Therefore,the analogous hyperbola model is further development of key strata theory.