In this thesis first, a formulation of a spectral element for a cross-ply laminated composite plate has been presented. Then spectral element model for a composite plate with active constrained layer damping (ACLD) has been developed. The spectral finite element method (SFEM) formulation in this thesis begins with deriving the fully coupled dynamic equations of motion by using Hamilton’s principle. Unlike the 1-D beam structures, two-dimensional (2-D) plate structures show much more complicated wave characteristic.Therefore, in this thesis, the spectral element modeling has been introduced only for the levy-type laminated composite plates and the plate 2-D problem has been transformed to the equivalent beam-like 1-D problem. Using finite strip method (FSM) the plate has then been considered as a connection of several strips (spectral plate element) with the joint node line along which the equivalent line load acts. The spectral plate element has been formulated with the exact solution to of a set of the equivalent 1-D coupled dynamic equations of motions in the frequency domain. This exact solution has been used as interpolating function for spectral element formulation. Then the spectral plate element matrix (dynamic stiffness matrix) has been formulated from the relations between the forces and displacements along the opposite two parallel edges. Finally, the frequency domain responses have been transformed to time domain using inverse fast Fourier transform (IFFT). In this research both free vibration and forced vibration is performed using the formulated elements for a cross-ply laminated composite plate. The high accuracy of the spectral element model has then been verified by corresponding results from conventional finite element solutions and exact analytical solutions, natural frequencies and the dynamic response to high frequency transients. The results are indicated that spectral finite element method can model structural dynamic characteristics with smaller element and higher accuracy in comparison with the results of the conventional finite element method. The SFEM formulation of an ACLD plate has been verified with the analytical solution. In addition the performance of an ACLD plate is investigated with proportional-derivative controller and the results obtained indicate that the ACLD treatments are very effective in damping the structural vibration as compared to the conventional PCLD. This is particularly true at low frequencies when proportional controllers are used and over a wider frequency ban when the controllers are augmented with a derivative component. Key Words: Structural Dynamic, Laminated Composite Plates, Spectral Finite Element Method, Spectral Element Matrix, Dynamic Shape Function, Active Constrained Layer Damping, Finite Strip Method, Proportional-Derivative Controller.