In this talk, two different spectral element methods (SEMs) extremely suitable for the numerical analysis of multifunctional materials will be presented, namely, the Doyle-type SEM and the Patera-type SEM [1-4]. The Doyle-type SEM uses the exact solutions of the governing partial differential equations (PDEs) to construct the shape or interpolation functions and to derive the corresponding spectral element matrix. Its semi-analytical nature results in an extremely high computational accuracy and efficiency, but its applicability is primarily limited to one-dimensional (1D) boundary value problems. On the other hand, the Patera-type SEM, which is in fact a higher-order FEM, is suited not only for 1D but also for two-dimensional (2D) and three-dimensional (3D) boundary value problems. The conventional FEM typically uses low-order shape functions and uniform node distributions, whereas the Patera-type SEM utilizes higher-order Lagrangian shape functions and a Gauss-Legendre-Lobatto (GLL) node distribution. In addition, a novel time-spectral boundary element method (TSBEM) will be also briefly presented [5], which utilizes the static fundamental solutions and an orthogonal Legendre polynomial expansion technique for the time-discretization of the unknown physical field quantity in conjunction with a spectral integration scheme. Representative numerical examples will be presented and discussed to demonstrate the advantages and disadvantages, accuracy and efficiency of the two different SEMs for the heat conduction and elastic wave propagation analysis of multifunctional materials and structures.