This paper discusses a hybrid ray–mode (wavefront–resonance) approach to analyze wave radiation and scattering by fluid loaded targets with internal structures. The approach consists of the following three methods: (1) coupling of plate and shell modes at joints and junctions; (2) spectral approaches (such as ray asymptotics, collective rays, guided modes, resonances, ray modes, etc.) for separable and weakly nonseparable structures; (3) a combination of methods (1) and (2) for nonseparable structures. The general theory is applied to a prototype structure of revolution consisting of a cylindrical pipe, hemispherical endcaps, a bulkhead, and a rib. First a conventional surface ray–normal mode approach is applied to the normal coordinate of each shell element, reducing the submerged structure into an equivalent multilayer–multiwave medium in the lateral domain. A matrix Green’s‐function formulation is then employed to systematically synthesize the acoustic radiation or scattering returns in terms of angular spectra of surface modes of the structural elements. This allows efficient bookkeeping of various spectral objects such as ray, collective ray, modes, ray–mode, resonance, etc., to be maintained.