There are various forms of clearance at the connection of various parts of the hydraulic support. However, the influence of clearance has been ignored in various related research studies of the hydraulic support. In order to clearly grasp the accurate impact contact response law between coal gangue and the hydraulic support, the radial clearance in the pin shaft connection structure of the tail beam is considered for the first time in this paper. By constructing the theoretical contact model of the pin shaft connection, the difficulty of studying the interaction between coal gangue and the hydraulic support through theoretical solution is proved. On this basis, the finite element contact simulation analysis method is proposed to study the impact contact behavior between coal gangue and the tail beam. This paper constructed the finite element impacting simulation model between coal gangue and the radial clearance-contained tail beam structure and carried out impact contact simulation between coal gangue and the multiple clearance-contained tail beam structure as well as the changing clearance-contained tail beam structure, respectively, and contact responses of the tail beam structure such as the spring stress, the pin shaft test point stress, acceleration, and velocity of the tail beam test point under different working conditions are obtained. The influence law of clearance on different contact responses is studied, and the differences of contact responses after coal gangue impact between two clearance-contained tail beam structures and three clearance-contained tail beam structures are compared and analyzed. Research results show that, in the condition of multiclearance, the amplitude of each contact response when gangue is impacted is greater than that of coal. When the radial clearance of the connection unit increases from 0 to 0.25 mm, the overall fluctuation amplitude of the contact responses decreases. In 3-clearance state, increase of the radial clearance size of the connection unit will lead to the increase of the spring stress, the stress of the pin shaft test point, and the velocity of the tail beam test point gradually and the decrease of the acceleration of the tail beam test point. Throughout the research, the vibration response of the pin shaft can be taken as coal gangue recognition parameter. The work provides a theoretical basis for the study of the influence law of clearance on hydraulic support and provides a reference for the study of contact behavior between coal gangue and the hydraulic support.