A wave solution has been obtained for the acoustic fields inside a class of perfectly focusing spherical lenses that have been previously described by Luneberg and Gutman. Plane‐incident radiation on a lens having a continuous radially varying refractive index, prescribed by Gutman, is assumed. The radial functions for the eigenfunction expansion are defined by an integral solution of the radial portion of the separated scalar Helmholtz equation for the interior of the lens. This defining integral leads immediately to recurrence relations that are useful in the computations. The integral may also be evaluated asymptotically for large wavenumber‐aperture products, for functions of low order, in order to normalize suitably the sequences of functions generated recursively. Axial and polar patterns were obtained for various lenses for wavenumber‐aperture products up to 240.