History-dependent and history-independent models of magnetic hysteresis are proposed. Spline approximations to the magnetization curves make these models applicable to major loops of any shape. The H(B) representation of reversal curves permits the development of a method that generates reversal curves guaranteed to be free from nonphysical negative slopes and excursions outside the major loop. The applicability of the models to electrical steels and a powder core is illustrated. © 1986-2012 IEEE.