An analytical investigation of the effects of boundaries on the damping of plates by constrained viscoelastic layers has been carried out as an extension of earlier work [E. M. Kerwin, Jr., J. Acoust. Soc. Am.31, 952 (1959)]. It is assumed that the plate is in vibration with straight‐crested one‐dimensional flexural waves. Various geometries of plate and constraining layer are considered: infinite, semi‐infinite, and finite plates; and semi‐infinite and finite constraining layers. Boundary conditions considered are: supported, free, and clamped for the plate, and free and clamped for the constraining layer. By calculating the energy dissipation near the boundary relative to what it would be far from the boundary, a measure of the damping efficiency near the boundary may be obtained. Such energy ratios are presented for the various cases. It is found that the local dissipation near the boundary can be either greater or less than the “far‐field” dissipation. These edge effects occur principally within the first half wavelength from the boundary. Numerical calculations were carried out on a high‐speed digital computer. [This work was supported by the U. S. Air Force, Wright Air Development Center (subcontract from the University of Minnesota), and by the U. S. Navy, Bureau of Ships.]