The curvilinear motion in a vertical plane is one of the most important features of the supercavitating vehicle.It is of great significance to study the controllability and the maneuverability of the supercavitating vehicle.Models are built for the effects of the angle of attack,the gravity and the inertial force in the curvilinear motion in the vertical plane.Numerical simulations are carried out for the supercavity motion based on these models combined with the Logvinovich model.It is shown that the maximum deviation displacement in the outward normal direction of the trajectory with a constant curvature,which occurs in the tail of the supercavity,increases as the cavitation number or the curvature radius of the supercavity trajectory decreases under the condition that other model and flow parameters are kept constant.For a varied curvature,the supercavity shape changes evidently because of the change of the ambient pressure,but with the same trend as in constant curvature.The deviation displacement increases along the supercavity length gradually.