The pitching motions of supercavitating vehicles could not be avoided due to the lost water buoyancy.In order to have some insight for the design of the supercavitating vehicles,the fixed frequency and free pitching motions are investigated.A numerical predicting method based on the relative motion principle and the non-inertia coordinate system is proposed to simulate the free pitching motions of supercavitating vehicles in the longitudinal plane.Homogeneous and two fluid multiphase models are used to predict the natural and the ventilated supercavitating flows.In the fixed frequency pitching motions,a variety of working conditions are considered,including the pitching angular velocities and the supercavity scales and the results are found to be consistent with the available experimental results in literature.The mesh deformation technology controlled by the moment of momentum equation is adopted to study the free pitching motions and finally to obtain the planing states proposed by Savchenko.The numerical method is validated for predicting the pitching motions of supercavitating vehicles and is found to enjoy better calculation efficiency as comparing with the mesh regeneration technology. The pitching motions of supercavitating vehicles could not be avoided due to the lost water buoyancy. In order to have some insight for the design of the supercavitating vehicles, the fixed frequency and free pitching motions were investigated. A numerical predicting method based on the relative motion principle and the non-inertia coordinate system is proposed to simulate the free pitching motions of supercavitating vehicles in the longitudinal plane. Homogeneous and two fluid multiphase models are used to predict the natural and the ventilated supercavitating flows.In the fixed frequency pitching motions, a variety of working conditions are considered, including the pitching angular velocities and the supercavity scales and the results are found to be consistent with the available experimental results in literature.The mesh deformation technology controlled by the moment of momentum equation is adopted to study the free pitching motions and finally to obtain the planing states proposed by S avchenko. numerical method is validated for predicting the pitching motions of supercavitating vehicles and is found to enjoy better calculation efficiency as comparing with the mesh regeneration technology.