Structural members exhibit hysteretic behavior under cyclic loading. Among the hysteresis models available in the literature, the differential model proposed by Bouc-Wen is most widely used, owing to its robustness. This model involves many parameters that define the shape of the hysteresis loops. Estimating these unknown parameters is an identification problem that can be tackled by optimization algorithms by using prediction error as the objective function. Stochastic methods like simulated annealing and genetic algorithms can help find global minima but at a high computational cost. Here, the homotopy technique is employed to identify the unknown parameters. The efficiency of this technique in identifying the parameters of the Bouc–Wen model is demonstrated with examples. The present approach is then compared with global optimization methods, such as genetic algorithms and particle swarm optimization techniques. Numerical results confirm that the homotopy method is superior in terms of computational effort and convergence efficiency. © 2020 Taylor & Francis Group, LLC.