Abstract: The transfer function matrix of a beam with damping isderived by means of spectral element method (SEM). The analytical solutionfor a one-dimensional beam is applied in the form of shape functions in continuousform. Compared to the finite element method, the spectral element methodcan be used to obtain high precision with less degrees of freedom and elements.The proposed transfer function is represented by the transcendental functionwith geometrical and physical parameters of the beam, and is different fromthe traditional transfer function, represented by modal parameters. A newmethod to identify physical parameters of a beam structures based on thegenetic algorithm is proposed. Two numerical examples of cantilever beamswith varying cross section are given to show the effectiveness of theproposed method.