The reflection, refraction, and transmission characteristics of a plane electromagnetic wave incident from an isotropic medium, through a moving uniaxial slab, and into another isotropic medium are studied. The conceptual equivalence of a moving medium and a stationary anisotropic one with suitably defined permittivity and permeability tensors is used for the analysis. Complete field expressions are obtained in all three regions for an arbitrary orientation of the plane of incidence and an arbitrary angle of incidence. Special cases where the plane of incidence is parallel, or perpendicular, to the direction of slab motion are considered for both an incidentEwave and an incidentHwave. Some interesting numerical results are presented for the transmission coefficient at normal incidence when the moving slab is a magnetoionic plasma subject to a strong magnetic field and when the moving slab is a uniaxial crystal.