It is one of the most important stable motion modes to move with tail-slaps for supercavitating vehicle. The periodical tail-slaps provide lift and restoring moment to keep a dynamic equilibrium of the vehicle. Research on the mode is significant to the stability and controllability of supercavity and its vehicle. The effect of the tail-slaps on supercavity is modeled to establish a supercavity model, combining with effects of gravity and angle of attack (AOA). Hydrodynamic forces acting on the vehicle are also formulated in the longitudinal plane based on the supercavity model and rigid body dynamics, considering its tail-slaps and control surfaces. The vehicle, which has a fixed periodical tail-slap, is simulated to calculate its hydrodynamic forces at a constant horizontal speed for different maximum pitch angles using the cavitation number embedded coefficient correction algorithm. The supercavity model is finally verified to some extent by comparing numerical results with experimental ones.