The reflection and transmission of electromagnetic waves by a moving dispersive dielectric half‐space or slab are investigated theoretically. The dispersive medium is assumed to be a cold plasma medium. Two cases of the movement are considered: (a) the plasma medium moves parallel to the interface; (b) the plasma medium moves perpendicular to the interface. The electric vector of the incident wave is assumed to be polarized in the plane of incident (parallel polarization). Unlike the normal polarization case which was treated earlier, the reflected and transmitted fields for the present case are functions of the velocity of the moving plasma medium for both cases (a) and (b). An illustrative numerical example is given for case (a) at normal incidence.