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A higher-order theory is developed for composite box beams with rectangular, closed cross-sections. Each cross-section is therefore divided into two flanges and webs. Displacement representations are chosen for each part separately. The in-plane kinematics is 2 nd order for the flanges and even 3 rd order for the webs. The kinematics of the four parts is interconnected with the help of geometric coupling. All in-plane stress components can be obtained directly by using a reduced stiffness matrix for each single layer. The layups of the laminates for the flanges and webs are independent from each other. Only a symmetric layup with balanced angles is necessary. The determined differential equation system of 2 nd order including four independent functions can be solved completely in a closed-form analytical manner. As an actual example a cantilever beam under combined bending moment and transverse force is considered. The results obtained by this new theory are compared with the results of a FEM-model with a very fine shell element discretization.