The deformed cylinder method is a very versatile model that can be used on a wide range of acoustic scattering problems. To date, it has been applied to axisymmetric bodies of circular cross section, whether it be rigid, an elastic solid, or a shell. In this paper, the method is applied to nonaxisymmetric bodies of parabolic cross section. Results are given for the backscattering from a tapered finite rigid parabolic cylinder and are found to be in good agreement with estimates obtained using the Kirchhoff (physical optics) method.