The dynamic instability of interior ring stiffened composite shells under hydrostatic pressure is investigated. A shell structure such as a submarine vessel can undergo suddenly applied overpressure or successive shocks. In the presence of imperfections, the dynamic instability so triggered leads to a reduction of the load carrying capacity of the shell from that associated with quasi-static loading. Further, the large amplitude vibrations that occur prior to reaching the dynamic limiting pressure can have a damaging effect on the material of the shell. An asymptotic procedure is used in conjunction with p-version finite elements to extract the buckling mode and the associated second-order field. A single differential equation involving cubic nonlinearity is developed to characterize the dynamic behavior of the shell structure. This is solved by the Newmark method for time step integration along with Newton-Raphson iterations. Attention is focused on the reduction of the buckling pressure of the shell under dynamic loading, as well as the shell response at various increasing load levels until the displacements become unbounded.