Multi-directional fiber-reinforced composites are often used in aerospace structures. The design of such structures needs a realistic macroscopic stress/strain relationship for the composite material. In this paper an analytical approach for determining this stress/strain relationship is developed which is based on detailed analysis of the microscopic stress/strain fields, which govern the spread of plastic strain and the amount of material damage. In this approach, the heterogeneous composite is transformed into a homogeneous solid by Eshelby's equivalent-inclusion method (Mura, T., Micromechanics of Defects in Solids. Martinus Nijhoff, The Hague, 1982). 1 The microstresses and strains are then analyzed by using Lin's method of analyzing the microstress fields of elastically homogeneous polycrystals of periodic crystal orientations based on Green's functions of an infinite solid (Lin, T. H., Adv. Appl. Mech., 1971, 11, 255–311). 2 The major advantage of the present approach is that it does not need to isolate a representative volume (or ‘unit cell’) and specify the unknown boundary conditions. A numerical example for a cross-plied boron aluminum composite is given.