The Bouc-Wen class models are widely used to portray different types of hysteretic behavior. This paper presents an effective genetic algorithms-based method for fitting a generalized Bouc-Wen model, proposed by Song and Der Kiureghian [2006, “Generalized Bouc-Wen Model for Highly Asymmetric Hysteresis,” ASCE J. Eng. Mech., 132 (6), p. 610618], to highly asymmetric experimental hysteretic loops. The performance function is based on integral relationships derived from the generalized Bouc-Wen differential equation for each of the six different phases of asymmetric hysteretic loops. The conditions, which must be satisfied by the model parameters to obtain closed and smooth hysteretic loops, are specified. The method is applied to fit the generalized Bouc-Wen model to hysteretic loops, which are obtained in laboratory experiments for a new type of mounts used for base isolation of forging hammers. By using a single degree of freedom (SDOF) system with the predicted hysteretic characteristics, a remarkably close agreement between the measured and simulated vibrations of hammer was obtained.