Theoretical and experimental investigations are made to study the damping effectiveness of partially applied unconstrained layer damping treatments on rectangular plates having central rectangular cutouts. The effect of such partial applications on the modal frequencies, loss factors, and mode shapes are estimated analytically by the finite element method. Different partially applied damping configurations have been studied with a view to realize maximum system damping for the minimum mass of the applied damping. The theoretical results are validated by suitable experiments. Specific recommendations are made for the near optimum distribution of the damping material on the panel surface which is effective for many modes of the panel response. © 1986.