Numerical methods for predicting acoustic scattering from cylindrical shells generally consist of large finite element models of the shell coupled with finite element or integral representations of the fluid. In order to reduce the computational effort, the fluid can be represented by doubly asymptotic approximations [T. L. Geers and C. A. Felippa, J. Acoust. Soc. Am.73,1152–1159 (1983)]. The accuracy of first‐and second‐order DAA's is demonstrated for the two‐dimensional scattering problem of a plane acoustic wave incident on a thin cylindrical shell with and without an attached oscillator. Quantities compared to the exact solutions are fluid modal impedance and farfield radiated pressure. By appropriately adjusting a parameter value in the second‐order DAA, the impedance and pressure can be determined with reasonable accuracy. The first‐order DAA is demonstrated to be not as accurate. The effect of the oscillator on the radiated pressure is also discussed.