For analysis purposes, a multi-path core is divided into legs (a toroid is a single-leg core); flux-switching models for a leg are calculated from material parameters and leg geometry. These models include: (1) static φ(F) curve, assuming hyperbolic B(H) functions; (2) elastic switching in saturation, φε = ∊FR, where ∊ = ∊(F); (3) inelastic switching, φ = ρ(F-F0), where ρ = ρp[1−(φ/φs)2] for a constant-width leg; (4) ρt(φ) of a tapered leg; and (5) the average ρ and ρt for partial and full switching.