Abstract: Multi-transmitting formula (MTF) is considered to be a universal local artificial boundary condition, which is generally employed in finite element simulation of near-field wave motion. Due to the great difference between spectral element method (SEM) and finite element method (FEM), the traditional numerical scheme of MTF cannot be simply adopted in SEM without any change. In order to make use of the advantages of MTF, i.e., clear physical mechanism and controllable accuracy, basic problems involved in the combination of MTF and SEM are discussed in this paper, then the feasibility of spatial or temporal interpolation schemes are investigated, respectively. From the view of spatial interpolation scheme, a set of numerical formulas of MTF based on Lagrange polynomial are proposed, where the higherorder MTF is implemented via a simple iteration process. The accuracy and stability of the above MTF schemes are examined by a standard 1-D spectral element model of wave motion. The numerical results show that all schemes have comparable accuracy for 1st-and 2nd-order MTF, and the MTF scheme based on spectral element displacement mode is superior to others for 3rd-or 4th-order MTF. On the contrary, the stability threshold descends with the growth of interpolation polynomials' order of different MTF schemes, but instabilities only occur under the unusual condition that artificial wave speed is far beyond the physical wave speed.