Part I of this paper presents a dynamic model of magnetically-levitated (maglev) vehicle/guideway interaction. The vehicle employs a superconducting electromagnetic suspension system with canted magnets to provide simultaneous levitation and guidance in the face of guideway irregularities and cross-wind gusts. The dynamic simulation model includes a five degree-of-freedom nonlinear vehicle model, a superconducting magnet model, and a multi-span flexible guideway model. The formulation accounts for the dynamic loading on the guideway due to time-varying, distributed magnetic forces imposed by the vehicle. The maglev vehicle/guideway model is the basis for designing and testing a proposed preview control strategy in Part II of this paper.