Convex and probabilistic model solutions are obtained for multimode dynamic buckling of cylindrical shells with uncertain imperfections under symmetric radial impulsive loads. It is found that the maximum possible buckling deformations for any imperfection within uniform bounds ± δˆ can be made comparable to the buckling deformations from the probabilistic models at a reliability of about 99.5 percent. Numerical evaluation and interpretation of the convex model is much simpler than for the probabilistic models, and the convex model solution provides means for quality control of each and every shell by simply recording δˆ from appropriately filtered imperfection measurements. The power and simplicity of convex modeling for multimode buckling shows promise for more complex problems than require finite element modal analysis.