The three‐dimensional transient interaction of spherical acoustic waves with a cylindrical elastic shell is investigated using the concept of fictitious Riemann surface. Integral transform techniques are used. The transform double integrals with respect to the two shell coordinates are evaluated asymptotically by the method of “critical points.” Simple expressions for the early‐time responses of the shell and the scattered wave are obtained. The results of this investigation show that the effects of the curvature of the incident wave are quite significant with respect to the bending moments of the shell.