Analytical models are developed to predict the response of circular, fully clamped, orthotropic elastic plates to loading by a planar, exponentially decaying shock wave in water. The models consider the propagation of flexural waves in the plates as well as fluid–structure interaction prior and subsequent to water cavitation. The analytical predictions are compared to those of detailed dynamic FE simulations and the two are found in good agreement. It is shown that an impulsive description of the loading can lead to large errors. A comparison of the responses of cross-ply and quasi-isotropic laminates shows that the composite layup has a minor influence on the underwater blast performance. Design charts are constructed and used to determine plate designs which maximise the resistance to underwater blast for a given mass.