A new concept for the background in resonance scattering of acoustic waves by a submerged target is proposed. The idea is that the remainder after removing only the resonances from the target response must be used as the background. The complex wave numbers whose imaginary parts are the attenuation coefficients of elastic bulk waves in target are introduced to damp out the resonances. From the assumption that the structural damping coefficient, the product of the attenuation coefficients of elastic bulk waves, and the outer radius of target, is a large constant compared with the radiation damping coefficients of resonances, a simple mathematical expression is derived for elastic cylindrical shells and named the inherent background. It is shown that the inherent background leads to the impenetrable (i.e., rigid or soft) background in some limiting cases and also describes exactly the background of elastic shell over entire frequencies regardless of shell thickness.