In this investigation, the dynamics of soil-structure interaction (SSI) in frequency domain is investigated. The spectral element method is devoted to study free vibrations of Euler-Bernoulli beam resting on general elastic restraint at the ends and continuous springs against rotation and translation. Thus, partial differential equation of the motion is derived and upon solving the eigenvalue problem, natural frequencies are tabulated for the first three modes of vibration. Obtained results are regrouped in (1) the modal analysis of beams on elastic transversal or rotational rigidities of the continuum under foundation, (2) the influence of properties of elastic medium on the beam dynamic response (3), and the influence of non classical boundary conditions. In consequence, various results of above phenomena are described and commented.