Resonant scattering of flexural waves in acoustic waveguide is analysed by using the recursive transfer method (RTM). Because flexural waves are governed by a fourth-order differential equation, a localized wave tends to be induced around the scattering region and dampening wave tails from the localized wave may reach the ends of a simulation domain. A notable feature of RTM is its ability to extract the localized wave even if the dampening tail reaches the end of the simulation domain. Using RTM, the enhanced reflection caused by a localized wave is predicted and the shape of the localized wave is explored at its resonance with the incident wave.