Abstract: Theoretically, the extraction of resonance scattering spectra is performed by a pure elastic scattering function, which is defined as difference between the total scattering function and an appropriate background term. In this paper we derive a simple and explicit expression of the pure elastic scattering function for the separable geometries immersed in water. It depends on the modal mechanical impedance and acoustic impedance except a phase factor only relative to the geomatry. Analysis made with the new expression leads to find the two types of resonance with distinguishable character:the elastic-borne wave resonance and the fluid-borne wave resonance. The former depends mainly on elasticity of the object and the fluid-loading has secondary effect. The latter is related closely with the liquid-loading and vanishes if the liquid-loading vanishes. This allows us to classify the family of individual resonance correctly. Taking into account the contributions of the fluid-borne wave resonance, we modify the conventional resonance scattering formula by use of the Singularity Expansion Method.