Abstract: This paper proposes an effective research method for the dynamic characteristics of pyramid lattice sandwich beams on elastic foundations. The displacement function of the sandwich beam was derived, and the stress-strain relationship of the upper and lower beams and the pyramid core was established. The Rayleigh-Ritz method combined with orthogonal polynomials is used to derive the modal function of the sandwich beam under elastic support. The Hamilton principle was used to derive the motion equation of the structure, and the eigenvalue method and Newmark integral method were used to complete the dynamic analysis of the pyramid sandwich beam structure under elastic support. The natural frequency of the structure calculated by the theoretical method is compared with the finite element simulation results to verify the correctness of the theoretical model and discuss the influence of the elastic foundation on the amplitude-frequency response of the structure.