ESDU 85012 introduces a Fortran program for the estimation of the material damping in a rectangular@ laminated plate@ with simply-supported or clamped edges@ vibrating in the lower frequency natural modes (up to the fifth mode). The procedure applies when laminae having the same material properties and orientations of their principal axes of orthotropy are symmetrically disposed about the mid-plane of the plate. Beam characteristic functions are used to define the mode shapes@ and the analysis sums the contributions to energy dissipation from each lamina. The input includes individual lamina elastic properties@ the calculation of which is treated in ESDU 83035@ and damping properties. Curves are given to enable approximate values of damping in longitudinal and transverse flexure and in longitudinal shear to be estimated for each lamina. Guidance is given on the effect of various factors on the damping of fibre-reinforced laminated plates@ and a practical worked example illustrates the use of the method. The program is available on disc (uncompiled) in the software volume as ESDUpac A8512.