Fully three‐dimensional Green’s functions are important for synthesizing the acoustic scattering response from submerged spherical shells due to excitation not only by actual radiating sources without special symmetries but also by induced sources on the shell which can characterize the effects of truncations or loadings of the empty undisturbed shell prototype. As in a previous two‐dimensional (2‐D) study of scattering due to axisymmetric (azimuthally independent) source configurations [J. M. Ho and L. B. Felsen, J. Acoust. Soc. Am.88, 2389–2414 (1990)], the goal is the derivation of self‐consistent hybrid ray‐mode asymptotic algorithms from appropriaterigorousalternative spectral representations; hybrid ray‐mode algorithms have been shown to be well matched to the wave phenomena which generate the scattered acoustic fields in the fluid in the mid‐ and high‐frequency rangeka≳5, wherekis the wave number in the fluid and ‘‘a’’ is the mean radius of the shell, and also under pulsed excitation. The presentation here deals with the rigorous spectral foundation, asymptotics, and ray‐acoustic interpretation of the rich variety of generic 3‐D wave phenomena encounteredonthe shell surface, which must be understood in order to treat the general case of arbitrary source and observer locations in a follow‐up paper.