A number of physical and semiempirical flux-switching models that have appeared in the literature are reviewed briefly and classified. A thin ferrite core is switched by essentially a step mmf (with short rise time Tr). Three components of the total are distinguished and semiempirical models are proposed for each : 1) an initial elastic spike during the rise time of , where ε is constant in time; 2) a decaying inelastic starting at , , where ρiand Ciare constants in time and is the static mmf threshold; and 3) the bell-shaped, main inelastic , where, for given is the peak of is the φ value on the static curve, and φsis saturation flux. Expressions involving switching parameters are given for , and φd. The agreement between these models and of a thin core is satisfactory. The main- model is applied in a numerical analysis of three magnetic circuits: an unloaded core, a core loaded by , and a diode, and a core-diode shift register. The agreement between computed and experimental results is satisfactory, especially if different parameters are used for computing step- and ramp- switching.