A new spectral element method is presented for the wave propagation analysis of frame structures. In this method, the Laplace transform is applied instead of the Fast Fourier Transform, which has been used in the original spectral element method. Numerical results showed that this method is practical and it can be a reference for the convergence criteria of wave propagation analysis by the conventional finite element method. NOMENCLATURE w(x,t) E I A p displacement of the beam Young's modulus second moment inertia of area area of cross section density strain energy ET kinetic energy Ew energy made by external forces ( ~ ( ), function values at the left end and the right end of the beam w, w, displacements at the left end and the right end rp, rp, slope at the left end and the right end N, N, external shear forces at the left end and the right end M, M, external moments at the left end and the right end s Laplace operator ca) Laplace transformed function c, · .. C 4 arbitrary constants of the general solution to the beam equation lf/, lf!, T., T, G J [K, (s)] u1 ···w2 8,,···8,, =~ solution to the characteristic function stiffness matrix of the spectral beam element nodal displacements for the rod element nodal forces for the rod element stiffness matrix of the spectral rod element nodal rotation for the torsional bar element nodal torsional moments for the torsional bar element shearing modulus torsional stiffness factor for the element cross section stiffness matrix of the spectral torsional bar element nodal displacements of the 3-D frame member nodal rotational displacements of the 3-D frame member nodal forces of the 3-D frame member M ,, ... M ,, nodal moments of the 3-D frame member [K(s)l stiffness matrix of the 3-D frame member {u} nodal displacement vector of the 3-D frame structure {F} nodal force vector of the 3-D frame structure [K(s)] global stiffness matrix of the 3-D frame structure