A general analytical method for determining the radiated sound fields from axisymmetric surfaces of arbitrary cross section with general boundary conditions is developed. The method is based on an integral representation for the external solutions of the Helmholtz equation. An integral equation is developed governing the surface potential distribution which gives unique solutions at all wavenumbers. The axisymmetric formulation of the problem reduces its solution to the numerical evaluation of line integrals by Gaussian quadrature. The applicability of the solution approach for both a sphere and finite cylinder is demontrated by comparing the numerical results with exact analytical solutions for both discontinuous and continuous boundary conditions. The method is then applied to a jet‐engine‐inlet configuration and the computed results are in good agreement with exact values.