Introduction The transverse (through-the-thickness) elastic properties of continuous fibre reinforced composite laminated plates@ of the type shown in Sketch 1.1@ are@ to a large extent@ dependent upon the properties of the matrix material used to bond the fibres together. For many matrix materials@ these properties can be very low compared with those in the direction of the reinforcing fibres@ with the result that significant deflections can be caused by through-the-thickness shear stresses which arise in plate bending. In order to take this behaviour into account@ it is necessary to obtain values for the shear stiffness terms that relate the transverse shear force resultants to the transverse shear strains. This Item together with the accompanying ESDUpac A8913 presents a Fortran computer program for the determination of these stiffnesses for laminated plates@ without restriction on the type of lay-up. The plates are considered to be built up from thin orthotropic homogeneous layers with perfect bonding between them. The layers may have different material elastic properties@ thicknesses and orientations of their principal axes of orthotropy. The analysis is also applicable to thick sandwich panels. This Data Item consists of three parts. Section 1 describes the theoretical solution to the title problem and its limitations in application to practical panels. Section 2 describes the input and output for the program of ESDUpac A8913 and gives example calculations.