ESDU 90016 introduces a Fortran program@ available on disc (uncompiled) in the software volume as ESDUpac A9016@ to estimate the lower natural frequencies of flat@ isotropic or orthotropic@ rectangular or square plates. Any combination of shear and direct loading@ uniformly distributed along the edges@ that is less than the buckling load may be used. All combinations of clamped@ simply-supported and free edge conditions may be considered. For orthotropic plates the principal axes of orthotropy should be parallel to the edges. The plates are assumed to be thin and the effects of shear deformation and rotary inertia are neglected. These assumptions are satisfactory when the ratio (half wavelength)/(thickness) exceeds 20. The Rayleigh-Ritz method of analysis is used in which plate displacements are represented by a finite series of orthogonal polynomial functions. The series used are sequentially derived from a starting polynomial function that satisfies the boundary conditions of the plate. Notes are included on the effects of in-plane loading on frequency and modes of vibration@ and are illustrated with sketches. The accuracy and limitations of the method are discussed. Typical comparisons are given of measured with estimated natural frequencies for isotropic and fibre-reinforced laminated plates under compressive loading. A full description of the input and output is included@ together with a flowchart and worked examples.