A mechanical representation of batoid-like propulsion using a flexible fin with an elliptical planform shape is used to study the hydrodynamics of undulatory propulsion. The wake is found to consist of a series of interconnected vortex rings, whereby leading and trailing edge vortices of subsequent cycles become entangled with one another. Efficient propulsion is achieved when leading and trailing edge vortices coalesce at the spanwise location where most of the streamwise fluid momentum is concentrated in the wake of the fin. Both the Strouhal number and the wavelength are found to have a significant effect on the wake structure. In general, a decrease in wavelength promotes a wake transition from shedding a single vortex per half-oscillation period to shedding a pair of vortices per half-oscillation period. An increase in Strouhal number causes the wake to bifurcate a finite distance downstream of the trailing edge of the fin into a pair of jets oriented at an acute angle to the line of symmetry. The bifurcation distance decreases with increasing Strouhal number and wavelength, and it is shown to obey a simple scaling law.