A spectral finite element model is developed to study scattering and transmission of axial-flexural-torsional coupled waves in multi-sitedelaminated thick composite beams. The analysis may find its suitability and superiority to capture the high frequency dynamics of laminated composite structure in vibrating environment and for health monitoring in combination with non-destructive test data. Spectral finite element considering first order shear deformation is used to model the delaminated segments along the span of the beam, as well as the delaminated ply-groups in thickness direction. This spectral element is derived from exact solution to the 3D governing wave equations in Fourier domain. As aresult, the thin sublaminates and beam segments do not lock. Spatial discretization is carried out in a similar way as in conventional finite element method. The major differences from conventional finite element method are (1) the transformation of all the fields from temporal to frequency domain is carried out using Fast Fourier Transform (FFT) algorithm, (2) the global system is solved at each frequency step (3) fine meshing at the delamination tip to capture the crack-tip singularity (as in conventional finite element discretization) is not required (4) the overall system size becomes many order smaller than that in conventional finite element methods. The study essentially includes unsymmetry induced due to ply orientations and due to multiple delamination across beam thickness. A case study is presented to show the effect of wave transmission and scattering by a single through delamination in unidirectional composite beam.