A new approach to the problem of electromagnetic wave propagation through a vacuum‐plasma interface is formulated and used to solve two simple antenna problems. First, the impedance of a spherical body covered by a vacuum sheath and immersed in a plasma is calculated. The result is found to coincide with the empirical formula commonly used so far. Second, a cylindrical antenna also isolated from the plasma by a sheath is studied. The antenna can support guided modes whose dispersion relation is derived. An experiment has been performed in order to verify this dispersion relation. Experimental results are found to be in favor of the present approach.