Theoretical and experimental investigations have been made to study the damping effectiveness of unconstrained partially applied damping treatments applied to rectangular plates. By using the finite element approach, different configurations of partially applied damping layer treatments have been analyzed for their effectiveness in realizing maximum system damping with minimum mass of the applied damping material. The effects of partial application on the modal frequencies, loss factors and mode shapes are discussed. 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 panel response. © 1985 Academic Press Inc. (London) Limited.