The boundary value problem involving a magnetized plasma half‐space confined by a perfectly reflecting interface is solved using the relativistic Vlasov–Maxwell system. The external field is assumed to be constant and along the normal of the boundary, and only the linear responses to obliquely incident vacuum waves are considered. When the incidence is normal, only a pair of purely transversal modes, similar to the ordinary and extraordinary modes of the infinite systems, can be excited. When the incidence is oblique, two additional hybridpandsmodes may exist, which are decoupled into the longitudinal and transversal parts only when there is no external field. Thepmode vanishes if the field at the boundary, B(0), is in the plane of incidence, and thesmode is zero if B(0) is in the plane which is perpendicular to both the interface and the plane of incidence. Reflection, transmission, and absorption coefficients are calculated for the case of normal incidence.