Abstract: Simulating the hysteresis characteristic of soft magnetic materials accurately and quickly is crucial for the electromagnetic field simulations, optimal designs and other aspects of motors, transformers, and etc. However, the classical Preisach hysteresis model involves complex double integral operation, making it difficult to meet the above requirment, and the only proposed analytical Preisach model has the problems of deduction mistakes and being not generic. To resolve these issues of the analytical Preisach model, the correct analytical Everett function is thereby deduced. Based on the analysis of Preisach basic principle, the key cause for considering the reversible magnetization component is thus analyzed, and accordingly a correct and general analytical forward Preisach model is proposed for the first time. The simulated hysteresis loops are compared sufficiently with the measured ones to verify the accuracy of the proposed model.