A study on optimal placement of constrained-layer damping (CLD) treatment for vibration suppression of plates is presented. A mathematical model is derived using the energy approach. This model allows both the constraining layer (CL) and the viscoelastic layer (VEM) to be either as thick as the host or very thin. The in uence of treatment thickness on damping e ects is particularly addressed. From the simulated results, it is found that the best damping performance occurs as the CL thickness is twice that of the VEM thickness. As to the optimization process, an objective function including structural damping ratios, resonant frequencies' shift, and CLD thickness is deΓΏned. In optimization, the structural damping plays the main performance index and the frequencies' shift and CLD thickness play as penalty functions. A topographical method in conjunction with the complex method is used to search for the global minimum. Examples are illustrated and the e ects of weighting factors are discussed. Individual e ects of weighting factors can be useful for designers, since the designers can build up a better sense of how CLD treatment improves the vibration suppression.