The dispersion relation for propagation of an electromagnetic wave between two semi‐infinite slabs of plasma is found under the assumption of infinite magnetic field along the slabs. Provided the plasma frequency is above the applied frequency, a fast wave solution exists, with a sinusoidal field distribution in the free‐space region between the plasma slabs, and exponential decay into the slabs. A complex plasma frequency is introduced to account for collision losses in the plasma, and substituting this complex plasma frequency into the dispersion relationship, the attenuation constant of the wave is found. The imaginary part of the plasma frequency is computed from collision theory and found to give damping considerably smaller than that obtained with metal guides. An application to high‐field linear accelerators is treated in detail.