Damping properties of viscoelastic composite structures are related to the thicknesses of their layers. To design these structures, there is a need to know their damping properties sensitivities according to the thicknesses of their layers. This allows to evaluate errors committed in the design for a layer thickness variation or to predict the damping properties of other structures having the same dimensions (length and width) except the layers thicknesses. Sensitivity analysis conducted to date are limited to the first derivative approximation which reduces considerably the calculation accuracy and the convergence radius but are computation time consuming. In this paper, we propose a high order continuous sensitivity analysis of the damping properties of viscoelastic composite plates according to their layers thicknesses. This method allows to get the exact values of the optimal damping properties and the high order derivative. Two cases are considered herein: the variation of only the thickness of the core layer and the variation of the thickness of each layer the total thickness of the structure being constant. Results showed that the damping properties variation is not standard but related to the viscoelastic material, the fibers orientation of the laminated faces, the boundary conditions and the structure dimensions.