Abstract: In recent years, hypersonic weapons have developed rapidly due to their advantages in attack speed and damage ability. In order to improve the space utilization of the platform, the adoption of variable cross-sectional warheads that have the same shape as the platform becomes an important developing trend. However, the increase in structural shape complexity and velocity results in extreme dynamic loading conditions, which lead to serious structural strength issues for warheads. To investigate the dynamic response of variable cross-sectional projectiles in oblique penetration scenarios, based on the free-free beam and structural plasticity theories, a dynamic response model and structural failure function with the coupling of axial force and bending moment considered were established for the conical projectile subjected to impact loading at its nose. Then, by means of Abaqus/Explicit nonlinear finite element analysis software, the dynamic responses of typical conical projectiles under different impact loadings at the nose were numerically simulated, and the rationality and accuracy of the proposed dynamic response model were verified. Based on the theoretical models, the influences of the structural parameters of projectiles, such as the shape coefficient of the projectile head, semi-conic angle, diameter-to-thickness ratio, as well as the length-to-diameter ratio were analyzed. The results showed that the theoretical model could predict the internal force distribution and failure locations of the conical projectiles very well. The nose mass of the projectile could decrease the magnitude of the internal forces, but does not change their non-dimensional distribution. When the impact loading, the diameter at the front part of the projectile, as well as the other nondimensional parameters keep constant, the increase of the semi-conic angle of the projectile induces a shift of the critical failure section toward the head, and the increase of the length-to-diameter ratio or diameter-to-thickness ratio makes the projectile more prone to structural failure.