Abstract Acoustic backscattered responses of typically structures were recently by the ‘Resonance Isolation and Identification Method’ (R.I.I.M.) applied to cylinders immersed in a fluid. Experimental measurements were performed within the final transient state itself, which is the particularly of this method. We propose an interpretation of the results, the basis of which relies upon the Resonance Scattering Theory, as developed by other authors. This paper puts forward the concept of ‘ S matrix elastic poles dominance’, which poles are associated with elastic surfaces waves. It is thus assumed that the S matrix elastic poles govern almost entirely the final transient state. Such an hypothesis allows us to state a first reasonable interpretation of the responses recorded by the R.I.I.M. The theoretical results explaining the experiments are rather simply formulated. The mathematical study described hereafter consists in an approach where both Fourier and Laplace transforms are used together. Other scattered signals than R.I.I.M. responses are also theoretically analysed. The response relative to frequency modulated signals is formulated and an approximate expression of the resonant term is given for an arbitrarily shaped incident signal.