A geometrically nonlinear model for general thin-walled open-section composite beams with arbitrary lay-ups under various types of loadings based on the classical lamination theory is presented. It accounts for all structural coupling coming from the material anisotropy and geometric nonlinearity. Nonlinear governing equations are derived and solved by means of an incremental Newton–Raphson method. The finite element model that accounts for the geometric nonlinearity in the von Kármán sense is developed to solve the problem. Numerical results are obtained for thin-walled composite Z-beam and I-beam to investigate effects of geometric nonlinearity, fiber orientation and warping restraint on the flexural–torsional response.