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Shape memory alloy actuators (SMA) show asymmetric hysteresis loops between the input current and output displacement. Furthermore, the SMA actuators exhibit saturated output displacement at maximum and/or minimum input. A generalized Prandtl-Ishlinskii model is formulated to model hysteresis nonlinearities of SMA actuators. In this model, a generalized play hysteresis operator is proposed and integrated with a density function to construct generalized Prandtl-Ishlinskii model. The formulated generalized Prandtl-Ishlinskii model can also describe hysteresis loops with saturated output displacement. The results suggest that unlike the classical Prandtl-Ishlinskii model, the proposed Prandtl-Ishlinskii can effectively characterize hysteresis nonlinearities of the SMA actuators.