Fano resonance is a phenomenon that is caused by interactions between continuous and discontinuous states. It was initially investigated in optical and atomic systems. Although flexural waves have seldom been discussed in association with Fano resonance, they have attracted increased interest because a numerical method, RTM (Recursive Transfer Method), has recently been developed under the framework of weak form discretisation. A flexural wave on an elastic waveguide is a typical biharmonic system governed by a fourth-order differential equation and it is a suitable subject for verifying the feature of RTM that can extract the localised/quasi-localised wave. The continuous and discontinuous states can be realised by the incident and localised waves in an elastic-waveguide scattering problem. When an elastic plate is cut from both sides, the resulting thin region works as a scattering region and the localised wave is generated there. Furthermore, RTM predicts that the shape modulation of the thin region will induce a change in the resonance curve. The purpose of this study is to demonstrate the asymmetric change of resonance curve through a scattering experiment with elastic waveguides made of aluminium. For this purpose, we propose an accurate procedure for extracting the S-parameters from the standing waves without needing to alter the fixed boundary condition as was unavoidable in the previous procedure. The data obtained by experiment are consistent with numerical results obtained by RTM, and control of the asymmetry in the resonance curve is demonstrated.