Due to kinematic function requirements, deployable structures inevitably have many clearance joints. The existence of clearance joints not only reduces the structural stiffness but also leads to complex nonlinear dynamic characteristics. This paper proposed a general numerical method based on the wave motion theory, which is able to analyze these complex nonlinear dynamic characteristics of frame structures with clearance joints. The dynamic model of frame structures with clearance joints is derived on the basis of continuous wave equations. The clearance joint is modeling by combining Lankarani and Nikravesh contact model with the Ambrósio friction model. The established dynamic model of frame structures is solved by the finite difference time domain (FDTD) method. A triangular frame structure with two clearance joints is taken as the numerical example for the verification of the proposed numerical method. Numerical results show that the longitudinal wave affects the distribution direction of contact positions and the transverse wave mainly affects the distribution range of contact positions. It has been also found that the introduction of torsional springs with reasonable pretension torque is able to significantly improve the distribution of contact positions and reduce state uncertainties of clearance joints in structural vibrations.