The radiation from an infinite dielectric slab fed by a line source has been calculated from a branch‐cut integral. The modal efficiency of the device as a wave guide is defined as the ratio of the power propagated in a mode to the sum of the modal and radiated powers. For a range of the parameters such that only one mode can be propagated, the modal efficiency has been plotted numerically. Except for extreme values of the parameters, the efficiency runs around 80 percent to 90 percent.The slab form is not one likely to be used in practice, but the efficiency of a cylinder would be expected to have about the same value.