Damping is an effective way of suppressing mechanical vibrations. Passive constrained and unconstrained layer damping patches are often used in the industry as damping solution for vibrations and acoustics problems. In this study, topology optimization methods were applied to the finite element models (FEM) of plates and damping patches in order to determine the critical locations for the frequency range of interest. For that purpose, MSC. Nastran SOL 200 optimization is used for both topology and thickness optimization. The structures are excited at single point and the acceleration of the plate at a pre-determined location is considered as output. The objective of the optimization is chosen as the minimization of the acceleration spectrum up to 500 Hz. The optimized damping patch topology is compared to the base plate with full application of damping patch on frequency response functions. The simulation results from topology and thickness optimization show that these methods can effectively improve the frequency response functions.