Approximate formulas for the complex propagation constant and characteristic field configuration for dielectric‐filled traveling wave slot antennas are obtained by a variational procedure. To set up the variational method, the generalized reciprocity theorem for traveling wave line sources is deduced; it differs considerably from the reciprocity theorem for point sources. A perturbation technique for solving the variational equations is given. Formulas are worked out for rectangular wave guides and good agreement with available measurements is obtained.