The computer program called Energy Stability in a Recirculating Accelerator (ESRA) Free Electron Laser (FEL) has been written to model bunches of particles in longitudinal phase space transversing a recirculating accelerator and the associated rf changes and aperture current losses. This energy-current loss instability was first seen by Los Alamos's FEL group in their energy recovery experiments. This code addresses these stability issues and determines the transport, noise, feedback and other parameters for which these FEL systems are stable or unstable. Two representative systems are modeled, one for the Novosibirisk high power FEL racetrack microtron for photochemical research, the other is the CEBAF proposed UV FEL system. Both of these systems are stable with prudent choices of parameters.