The dynamic response of both thick-walled and thin-walled cylindrical composite structures subjected to underwater impulsive loads is analyzed. In the case of thick-walled structures, a novel experimental setup, the underwater shock loading simulator (USLS), is used to generate the impulsive loads. Deflection and core compression are characterized using high-speed digital imaging. The experiments are supported by fully dynamic numerical calculations which account for fluid–structure interactions (FSIs) and damage and failure mechanisms in the materials. The analysis focuses on the effect of varying structural attributes and material properties on load-carrying capacity, deformation mechanisms, and damage. Results show that cylindrical sandwich structures have superior blast-resistance than cylindrical monolithic structures of equal mass with only relatively minor increases in wall thickness. In the case of thin-walled structures, a unique computational framework based on a coupled Eulerian–Lagrangian (CEL) approach is developed to study the structural collapse and damage evolution under large impulsive loads which induces an implosion event. Simulations are carried out for a range of hydrostatic pressure and impulsive load intensity, with different loading configurations. Ply level stress analysis provides an insight on the stress–structural deformation–damage evolution relationship during the severe explosion-induced implosion event. The experiments, computations, and structure–performance relations developed in the current study offer approaches for improving the blast-mitigation capabilities of cylindrical composite sections in critical parts of marine structures, such as the keel, hull, and pipes.