Abstract: Aimed at the dynamic instability problems of a supercavitating projectile subjected to an axial random load, a dynamic partial differential equation for the supercavitating projectile structure was established, and the dynamic stability was numerically calculated by Bolotins method. Considering the influences of the randomness of the structural parameters, the dynamic instability regions of the projectile were constructed by applying the random factor method, and the mean value and the variance of the boundary of dynamic instability regions were derived by using the algebra synthesis method. Based on the above, the non-probabilistic reliability of the projectile structure was analyzed. And the influences of stochastic parameters were discussed on the dynamic instability and non-probabilistic reliability of the supercavitating projectile. The computational results indicate that the parameter randomness can affect the dynamic reliability region boundary and non-probabilistic reliability. And the randomness of the geometric parameters has more influences on dynamic instability and reliability.