The deformed cylinder method is a very versatile model that can be used on a wide range of acoustic scattering problems. It may be applied to any axisymmetric body, whether it be rigid, an elastic solid, or a shell. Previous results obtained from this model have been restricted to broadside backscattering. This work is the first to verify the validity of the deformed cylinder method over such a wide range of shapes and material properties for angles close to broadside incidence. In order to determine the angular range from broadside over which the deformed cylinder method is valid, these estimates are compared with approximations from other techniques currently available. Agreement at angles of up to 30° from broadside was obtained for the rigid targets considered. The paper also shows that the deformed cylinder method produces reasonable levels for solid elastic bodies for up to 10° to 20° off normal incidence.