ESDU 03013 introduces a Fortran 77 program (ESDUpac A0313). The program calculates efficient flange and web thicknesses for a composite I-section beam to withstand up to 10 user-specified combinations of bending moment and shear force. The section is treated as thin-walled so that the flange and web thicknesses are small compared with the overall dimensions of the section@ that is its depth and width; those dimensions are prescribed by the user who also provides a minimum value of the overall flexural rigidity of the beam. The laminates that make up the beam are all of the same unidirectional composite plies layed up in O and/or + 45 and -45 layers. The connection between the web and flanges is made by continuing the web layers around to the inner faces of the flanges. In the first estimate of the thicknesses@ it is assumed that the applied bending moment is reacted entirely by the layers in equal thickness flanges and that the shear force is taken entirely by the web. That provides a starting geometry to which a more precise design procedure is then applied. In that procedure@ various heuristic design rules are employed@ using calculated values of reserve factors relating to strains across the section@ flange and web buckling@ and flexural rigidity. The procedure is iterative and is completed when all reserve factors lie between 0.99 and 1.05 inclusive. The program is provided in the form of a Fortran 77 source code and corresponding executable file.