The dynamic stability of thin, multi-layered composite shells reinforced by axial and ring stiffeners and subjected to pulsating loads acting in the axial direction is considered. The presence of a thermal field is shown to affect the location of dynamic instability regions in the load amplitude-frequency plane. The boundaries of these regions can be evaluated as functions of static critical loads, natural frequencies, and thermal terms; the latter can be easily calculated. This permits straightforward conclusions to be drawn regarding dynamic stability of shells for which the buckling and free vibration problems have already been solved. © 1990.