Comparisons are made between various estimates of the coupling coefficients that characterize the longitudinal wave contribution to acoustic scattering from thin elastic circular cylindrical and spherical shells. A common method of obtaining the coupling coefficient is through the application of the Sommerfeld–Watson transformation to the exact modal series solution. From this result, a high-frequency approximation can be derived that accurately describes the magnitude, but it does not adequately represent the phase. These are compared to coupling coefficients determined using a ray-theoretic approach. This representation describes both the magnitude and the phase well when compared to that obtained from the exact modal series result using the Sommerfeld–Watson transformation. [Work supported by ONR.]