The design of high-speed transportation tool cabins (chambers) such as automobiles, high-speed rail vehicles and large passenger aircrafts, has low-noise requirements. According to the lack of structural strength constraints for the existing optimization design of vibration and noise suppression of sandwich plates with viscoelastic core layers (SPVCL), research on design of SPVCL considering both structural strength/stiffness and vibration damping performance is carried out. In this paper, for the sandwich plates composed of composite materials and viscoelastic materials, simulation and theoretical analysis are adopted to study the mechanical and damping performance and the related optimization method: Firstly, based on the classical laminate plates theory(CLPT) analytical method (AM) for SPVCL is established; the influence of layers’ material and geometric parameters on structural mechanical properties by MATLAB is studied. Using NASTRAN software, a FEM model of SPVCL is established; modal strain energy (MSE) method and direct frequency response (DFR) method for obtaining modal damping are given; through the variable parameter calculation, the main factors affecting the damping performance of SPVCL are analyzed when considering the frequency-dependent characteristics of VDM. Finally, surrogate models are established based on response surface method (RSM), and through genetic algorithm (GA) a damping optimization for SPVCL constrained by the strength/stiffness of the structure is given, which can meet the requirements of structural safety and low vibration levels and have great significance for the suppression of the vibration and noise.