An electromagnetic waveguide in the earth's crust is idealized as a homogeneous lossy dielectric slab which is bounded by two homogeneous semi‐infinite conducting media. The source is a vertical electric dipole which is either above or below the upper surface of the horizontal slab. The exact integral formula for the field is evaluated by function‐theoretic means. It is shown that the dominant contributions are the propagating waveguide modes in the slab, although the lateral waves should not be ignored. The excitation of the waveguide modes and the relevant height‐gain and depth‐gain functions are also discussed. The attenuation characteristics of the modes are considered in some detail. It is shown that the principal loss mechanisms are the ohmic dissipation within the waveguide and the energy transmitted through the upper and lower walls into the bounding media. A numerical example is chosen where all three loss mechanisms are of the same order of magnitude.