Field configuration and resonant frequency are determined for the lowest azimuthally‐independent mode of a coaxial cavity surrounding a circular tube, Several values of the width of the coupling gap are considered, and the central problem consists in determining the tangential electric fieldEtin that gap. It was found that the fields near the axis of the accelerator are quite insensitive to the actual profile ofEt, and that satisfactory results are obtained by assumingEtto be constant. The problem is repeated for a parallel plane configuration, with the purpose of investigating the influence of the flattening of the cavity. Computations show that the two configurations yield fairly similar results.