A theoretical investigation of the electromagnetic waves due to a dipole source above a grounded dielectric slab has been made by integral transforms. The solutions in integral form have been evaluated asymptotically for distant field. It is found that the fields consist of a space wave and a surface wave. The former, spherical in nature, predominates in the free space, while the latter, cylindrical in nature and with a finite number of modes, is guided along the dielectric. As a result of the existence of at least one pole of the integrand, this surface wave always exists. At the dielectric surface, the zero‐order spherical wave has a null value except the case of critical thickness; then it should be referred to the next‐order solution.