A radial line slot antenna (RLSA) is a nonresonant multimode waveguide slotted array. The slot coupling to the radial waveguide in this antenna is analysed. A parallel plate waveguide with a periodic boundary condition is used to simulate a sectral region of the circular aperture in a RLSA. A set of integral equations for the fields in the slot is derived, based on the field equivalence theorem, and is solved numerically by Galerkin's method. Theoretical results effectively express the measured effects of the various antenna design parameters on the slot coupling.