ESDU 89011 introduces a Fortran program@ provided on disc (uncompiled) in the software volume as ESDUpac A8911@ that calculates the lower natural frequencies of rectangular thin plates (thickness/shorter dimension ratio less than 0.05)@ either flat or with shallow curvature (shorter dimension adius ratio very much less than unity). The input is structured to treat fibre-reinforced laminated plates particularly conveniently@ but will also deal with isotropic materials. The effects of a uniformly distributed in-plane biaxial loading can be included but@ if compressive@ should not exceed 30 per cent of the buckling load. In-plane shear is neglected@ as are shear deformation and rotary inertia@ and the method relies on small deflection@ linear plate theory. The program is restricted to plates in which the shear coupling terms in the stiffness matrix are zero. The program has been used to illustrate graphically for a typical laminated plate the effects of varying curvature and of varying the in-plane loading. The input format is explained in detail@ and a worked example illustrates it and the format of the output.