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ESDU 95028 introduces a Fortran program, ESDUpac A9528, to calculate the through-thickness stresses at and near the free edges of laminated plates. It is provided on disc in the software volume both uncompiled and compiled within ESDUview, a user-friendly shell that prompts on-screen for input data. A quadratic average stress failure criterion is suggested to predict delamination and the interlayer at which it occurs. It is based on the free edge stresses averaged over a distance from the edge; guidance is given on the choice of averaging distance, and the predicted onset of delamination is compared with test results extracted from the literature. The theory, which is presented in detail, assumes the plate is made 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 but must form a balanced lay-up about the mid-plane of the plate. The program will handle up to 50 different layer types and up to 500 layers, but both those numbers can be increased. The input to and output from the program are described with the aid of two fully worked examples, details of program testing carried out are included, and warning messages that may be provided are explained. Results for the stresses are compared graphically with test results extracted from the literature for finite element calculations of the edge stresses on six different plate lay-ups.