The optimal mechanical and geometric characteristics for layered composite structures subject to vibroacoustic excitations are derived. A Finite Element description coupled to Periodic Structure Theory is employed for the considered layered panel. Structures of arbitrary anisotropy as well as geometric complexity can thus be modelled by the presented approach. Damping can also be incorporated in the calculations. Initially, a numerical continuum-discrete approach for computing the sensitivity of the acoustic wave characteristics propagating within the modelled periodic composite structure is exhibited. The first- and second-order sensitivities of the acoustic transmission coefficient expressed within a Statistical Energy Analysis context are subsequently derived as a function of the computed acoustic wave characteristics. Having formulated the gradient vector as well as the Hessian matrix, the optimal mechanical and geometric characteristics satisfying the considered mass, stiffness and vibroacoustic performance criteria are sought by employing Newton׳s optimization method.