Among all aquatic species, mantas and rays swim by flapping their pectoral fins; this motion is similar to other fishes in terms of efficiency, but it gives better maneuverability and agility in turning. The fin's motion is featured by a traveling wave going opposite to the forward motion, producing a force thanks to momentum conservation. This article aims at understanding the swimming dynamics of rays, focusing on energy efficiency. A computational fluid dynamics (CFD) model of the swimming motion of a cownose ray has been implemented in openfoam, simulating the acceleration of the fish from still to the steady-state velocity using an overset mesh. In this analysis, the one degree-of-freedom dynamics of forward swimming is solved together with the fluid velocity and pressure. The effect of frequency and wavelength of fin motion on thrust, power, and velocity has been investigated and an analysis of the vortices in the wake showed has been performed. The energy efficiency of a self-propelled body has been defined in a novel way and it has been calculated for different motion conditions. The results showed that batoid fishes swim with high energy efficiency and that they are a promising source of inspiration for biomimetic autonomous underwater vehicles.