This article investigates reluctance-based dynamic models for multiphase coupled inductor buck converters. A reluctance-based state-space model is derived based on the inductance dual model of the coupled inductor. The physical core geometry is explicitly related to the circuit's dynamic properties to provide useful insights for coupled inductor design, especially if the number of phases is large. The transfer functions of multiphase coupled inductor buck converters with an arbitrary number of phases are derived based on the inductance dual model. It is shown that a symmetric multiphase coupled inductor buck converter can be modeled as a second-order dynamic system when perturbed with a common-mode duty cycle change, and the duty-cycle-to-output-voltage and duty-cycle-to-output-current transfer functions are determined by the leakage flux path of the coupled inductor. The differential-mode current balancing mechanisms of the multiphase coupled inductor buck converter are decoupled from other system dynamics and are determined only by the winding resistance and the magnetizing flux path. The applicability of the model in cases with structural asymmetry is discussed, with the results supporting the feasibility of scaling the coupled inductor structure to a large number of phases with tolerance for asymmetry. The dynamic models are verified by SPICE simulations and experimental results.