In an earlier paper [J. Acoust. Soc. Am. Suppl. 176, S9 (1984)] we developed the complete RST formulation for an elastic sphere in an elastic medium under shear and compressional wave incidences. We also showed how that work contained a variety of simpler cases that we have studied in the past, such as, a fluid‐filled cavity in an elastic matrix, an elastic sphere in water, a gas bubble in a liquid, etc, … as particular cases. We now develop the entire computational machinery of the RST and show the many useful plots that it can produce. These numerical displays include: (a) The SEM‐type poles with their relation to the various types of surface waves that they generate. The Franz‐zeros also fall under this category. (b) The graphs of the five types of scattering amplitudes (i.e.,fpp, fps, fsp, fss, ftt) that are pertinent to this elastic problem. (c) Their decomposition into partial waves or normal modes, (d) The decomposition of the partial waves into backgrounds and resonances, (e) The informative three‐dimensional plots of theresponse surfaceof all the scattering amplitudes, in the mode‐orderandfrequency domains, and, (f) The dispersion plots for the phase velocities of the various surface waves. All this is done for two material combinations (i.e., epoxy sphere in steel and steel sphere in epoxy) for which two different types of backgrounds are required to isolate the modal resonances. All displays are constructed in wide nondimensional frequency bands that include the resonance region for which λ≈a. Physical interpretations of all plots are given.