The dynamic instability associated with the interactive buckling of ring stiffened composite shells under hydrostatic pressure is investigated. An optimally designed shell has its static local and overall buckling pressures close to one another. The shell response is then governed by the nonlinear interaction between the modes, which makes the shell very imperfection sensitive. A shell structure, such as a submarine vessel, can undergo suddenly applied overpressure or successive shocks. In the presence of imperfections, the dynamic instability will be triggered which would lead to a reduction of the load carrying capacity of the shell from that associated with quasistatic loading. Further, the large-amplitude vibrations that occur prior to reaching the dynamic limiting pressure can precipitate some form of material failure. The dynamic interactive buckling analysis developed in this study is a combination of the amplitude modulation technique and the asymptotic procedure. The nonlinear differential equations of motion for the structure so developed are solved by the Newmark method for time step integration along with Newton-Raphson iterations. Significant reductions in the load carrying capacity of the shells are observed as a combined result of the dynamic application of the load and the modal interaction. Damping was found to be of marginal influence in enhancing the dynamic limit load. Interlaminar stresses accompanying the dynamic response are monitored, and these reach significant values prior to the onset of dynamic instability.