Cephalopods (i.e., octopuses and squids) are being looked upon as a source of inspiration for the development of unmanned underwater vehicles. One kind of cephalopod-inspired soft-bodied vehicle developed by the authors entails a hollow, elastic shell capable of performing a routine of recursive ingestion and expulsion of discrete slugs of fluids which enable the vehicle to propel itself in water. The vehicle performances were found to depend largely on the elastic response of the shell to the actuation cycle, thus motivating the development of a coupled propulsion-elastodynamics model of such vehicles. The model is developed and validated against a set of experimental results performed with the existing cephalopod-inspired prototypes. A metric of the efficiency of the propulsion routine which accounts for the elastic energy contribution during the ingestion/expulsion phases of the actuation is formulated. Demonstration on the use of this model to estimate the efficiency of the propulsion routine for various pulsation frequencies and for different morphologies of the vehicles are provided. This metric of efficiency, employed in association with the present elastodynamics model, provides a useful tool for performing a priori energetic analysis which encompass both the design specifications and the actuation pattern of this new kind of underwater vehicle.