A new mechanism-based phenomenological model, comprising linear and nonlinear springs and a nonlinear friction element, is presented for the pseudoelastic damping behavior of shape memory alloys. The use of a partial hyperbolic tangent friction element (a hybrid of an ideal and hyperbolic tangent friction element) is seen to increase accuracy in simulating experimental hysteresis behavior over earlier models. Comparisons are then made with existing models. Compared to the thermodynamic-based models, the present models have the benefit of not requiring calculation of austenite-martensite phase transformations. Unlike previously developed phenomenological models, the models presented herein have mechanical analogies that provide a strong physical basis, and clear relationships can be established between the unlocking of the friction element and the occurrence of phase transformation. These models are simpler and more intuitive than existing models.