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 T r ). Three components of the total \dot{\phi}(t) are distinguished and semiempirical models are proposed for each : 1) an initial elastic \dot{\phi} spike during the rise time of F, \dot{\phi}_{\epsilon} = \epsilon\dot{F} , where e is constant in time; 2) a decaying inelastic \dot{\phi} starting at t \cong T_{r} , \dot{\phi}_{rho i} = \rho_{i}(F - F_{d}^{min}) \exp [-(t - T_{r})(F - F_{d}^{min})/C_{i}] , where ρ i and C i are constants in time and F_{d}^{min} is the static mmf threshold; and 3) the bell-shaped, main inelastic \dot{\phi}, \dot{\phi} = \dot{\phi}_{p}{1 - [(2\phi + \phi_{s} - \phi_{d})/(\phi_{s} + \phi_{d})]^{2}} , where, for given F , \phi_{p} is the peak of \dot{\phi}, \phi_{d} is the φ value on the static \phi(F) curve, and φ s is saturation flux. Expressions involving switching parameters are given for \epsilon, \dot{\phi}_{p} , and φ d . The agreement between these models and \phi(t) of a thin core is satisfactory. The main- \dot{\phi} model is applied in a numerical analysis of three magnetic circuits: an unloaded core, a core loaded by R, L, C , 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- F and ramp- F switching.