Monte Carlo computer simulations have been performed in conjunction with free-energy perturbation calculations to determine the relative binding constants of four benzamidine inhibitors with trypsin. The protein backbone was constrained in the simulations, but sampling of the side chains was allowed. The calculated free energies are very precise and are shown to yield closed thermodynamic cycles. The calculations correctly predict p-aminobenzamidine to be the strongest inhibitor and give relative free energies of binding for p-methyl-and p-chlorobenzamidine in excellent agreement with experiment. The predicted overly weak binding of the parent benzamidine is most likely due to a deficiency in the partial charges. The relative binding affinities are justified in terms of bulk-solvation arguments whereby the more polar inhibitors are preferentially stabilized in water. The calculations demonstrate that Monte Carlo computer simulations can be used to determine accurate and precise relative binding constants for protein systems.