Dynamic pulse buckling of a single curvature composite shell under external pressure was examined using Lagrange's equation of motion and the Budiansky–Roth criterion. The predicted transient shell response compared very well with results from ABAQUS Implicit, and the predicted buckling loads also agreed with experiments on steel arches. Load duration determined whether the buckling was impulsive, dynamic or quasi-dynamic. Thicker composite shells were more likely to fail by first-ply failure rather than buckling. It was shown that the composite lay-up could be adjusted to increase the buckling resistance of the shell.