The state-space concept in conjunction with the Jordan canonical form is presented to solve the governing equations for the bending of cross-ply laminated composite beams. The classical, first-order, second-order and third-order theories have been used in the analysis. Exact solutions have been developed for symmetric and antisymmetric cross-ply beams with arbitrary boundary conditions subjected to arbitrary loadings. Several sets of numerical results are presented to show the deflected curve of the beam, the effect of shear deformation, the number of layers and the orthotropicity ratio on the static response of composite beams. (C) 1997 Elsevier Science Ltd.