A dolphin's biosonar may effectively discriminate subtle differences among targets. In order to investigate the possible physical mechanism of target discrimination, in this study, a finite element model excited by a biomimetic click pulse was proposed. The acoustic scattering field and stress distribution of a stainless steel shell were simulated. The biomimetic click experiments were then conducted to verify the theoretical predictions in an anechoic tank. The experimental results showed a good agreement with the model simulations. Furthermore, the elastic time-frequency features of three cylindrical shells with different wall thickness were obtained using a fractional Fourier transform filter to eliminate specular reflection and cross-term interference. To compare discrimination capacity of the time-frequency features with and without the specular reflection, a time-frequency correlator was applied to calculate the correlation coefficient between different shells. The results indicated that the time-frequency features can be represented in high resolution with less cross-term interference, and these features without specular reflection showed a good capacity to discriminate the shells with different wall thickness.