This paper presents two numerical realization of Preisach model by Density Function Method (DFM) and F Function Method (FFM) for a giant magnetostrictive actuator (GMA). Experiment and simulation showed that FFM is better than DFM for predicting precision of hysteresis loops. Lagrange bilinear interpolation algorithm is used in Preisach numerical realization to enhance prediction performance. A set of hysteresis loops and higher order reversal curves are predicted and experimentally verified. The good agreement between the measured and predicted curves shows that the classical Preisach model is effective for modelling the quasi-static hysteresis of the GMA.