In this paper we propose the FEM using a dynamic displacement function for the hydroelastic problem of a beam floating on shallow water in waves. Our dynamic displacement function consists of the Stoker's solution having 6 unknown coefficients, it means that each element needs 6 nodal data. What new nodal data are is derived by the Weighted Residual Method. This hydroelastic FEM gives stably calculating results in even high frequencies by dividing the beam into smaller elements. Numerical results show that: Wave response of relatively rigid beam is smaller than one of flexible beam. Wave response of floating beams have regular peak values but which are not resonance. Curvature at the central part of the beams have the upper limited value which relates to the bending rigidity.