Analytical predictions and finite element (FE) calculations are performed to predict the 1D response to underwater blast loading of sandwich plates with elastic cores, in contact with water on both sides and loaded by an exponentially decaying shock wave on one side. The theoretical models explicitly account for cavitation processes and effects of deep water, and their formulation helps identifying the governing parameters of the problem. Three characteristic regimes of behaviour are identified and regime maps are constructed. The analytical models are validated by FE simulations and used to explore the sensitivity of the predictions to the governing non-dimensional parameters. It is shown that, in the absence of plastic core deformation, sandwich plates with stiff cores are imparted higher blast impulses compared to those with softer cores and equivalent areal mass.