A computational model is used to examine the effect of caudal fin flexibility on the propulsive efficiency of a self-propelled swimmer. The computational model couples a penalization method based Navier-Stokes solver with a simple model of flow induced deformation and self-propelled motion at an intermediate Reynolds number of about 1000. The results indicate that a significant increase in efficiency is possible by careful choice of caudal fin rigidity. The flow-physics underlying this observation is explained through the use of a simple hydrodynamic force model and guidelines for bioinspired designs of flexible fin propulsors are proposed.