ESDU 94003 gives formulae for the in-plane and flexural stiffnesses of laminated flat plates built-up from thin orthotropic layers that may have different material properties, thicknesses, and orientations of their principal axes of orthotropy. The influence of the lay-up arrangement on the plate stiffnesses is explained. A complete list of possible forms of the stiffness matrices is provided with in each case examples of possible lay-up arrangements that will give them. Although it is normally convenient to use the central plane of the plate as the reference plane, subsequent calculations may be simplified by adopting another parallel reference plane; formulae are given for the values of the coupled in-plane and flexural stiffness matrix and the flexural stiffness matrix of the plate for such a shift of reference plane. The in-plane stiffness matrix is unaffected. A worked example illustrates the calculation of the stiffnesses. The relationship between the stiffnesses of a layer and the complete matrix of the elastic constants for an anisotropic solid is included. The relationship of the stiffnesses of both isotropic plates and sandwich panels with the laminated plate stiffnesses is also given. Equations are given relating the stress and strain in a layer in one axis system to those in another. The formulae apply to composite plates with systematic fibrous reinforcements in metallic or non-metallic matrices.