Abstract: In order to study the mechanical properties of the hard roof of the stope, based on the division of the coal seam into the plastic zone and the elastic zone, a transition zone describing the unyielding of the coal seam but exhibiting a yielding state with the upper direct top boundary is introduced. The direct roof and coal seam are regarded as the foundation, and the basic roof is regarded as the foundation rock beam. Using the theory of foundation beam and the theory of limit equilibrium zone, the differential equation and the base reaction force expression of the roof rock beam flexural curve based on elasticity, transition and plasticity are derived. On this basis, the relevant examples are operated and the corresponding simulation verification is performed using FLAC3D software. The results show that the numerical solution considering the basic reaction force of the transition part and the deflection of the roof rock beam is closer to the simulated value than the unconsidered, and the obtained result can be used for the analysis of the mechanical characteristics of the roof of the coal mine.