Taking the catamaran aircraft as the research object, this paper firstly proposes a method of modeling the multi-body dynamics of the catamaran aircraft based on force and moment constraints. Secondly, based on the modeling of multi-body dynamics, the influence of single fuselage elevator stuck fault of catamaran aircraft is analyzed, and the corresponding center wing stress mitigation strategy is proposed. Then, based on PID control method, the three-axis stability increment control law of catamaran aircraft is designed, and the rudder surface is reconstructed to solve the elevator stuck fault. Finally, a simulation analysis is carried out on the single fuselage elevator stuck fault of the catamaran aircraft. The simulation results show that the response of the multi-body dynamics model in the case of rudder plane failure is in line with expectations. In the case of small Angle stuck fault of the single elevator, maintaining the symmetrical side rudder plane can effectively reduce the stress of the center wing. The pitch response of the catamaran with increased stability during the pull-rod control is stable and in line with expectations.