Abstract: The rigid-structure method, Morison method and a method based on approximation of fundamental frequency are applicable simplified methods for the hydrodynamic force of incompressible non-viscous water. To investigate the differences of the above methods, the responsesof elastic cantilever circular piers were compared in the form of frequency domain transfer function, with the exact solutions which based on the radiation theory of incompressible non-viscous water considering structural deformation. Two kinds of size parameters were selected and 84 different sizes of piers were designed. By inputting impulse excitation, the transfer functions of displacement at the bottom, the transfer function of shear force and bending moment at the top were obtained. Then the first two order resonance-peak amplitude and resonance frequency were extracted for error analysis. Through the analysis of the range and variation trend of errors, it is found that:the resonance peak amplitude obtained by the rigid-structure method is more accurate, the resonance period obtained by the method based on approximation of fundamental-frequency is more accurate, and the error of the Morison method is significantly affected by the parameters. In addition, the amplitude of formant obtained by the fundamental frequency approximation is mostly smaller, while the amplitude and period obtained by the Morrison method are mostly larger.