A general geometrically nonlinear model for thin-walled composite space beams with arbitrary lay-ups under various types of loadings is presented. This model is based on the first-order shear deformable beam theory, and accounts for all the structural coupling coming from both material anisotropy and geometric nonlinearity. The nonlinear governing equations are derived and solved by means of an incremental Newton–Raphson method. A displacement-based one-dimensional finite element model that accounts for the geometric nonlinearity in the von Kármán sense is developed. Numerical results are obtained for thin-walled composite box beams under vertical load to investigate the effects of shear deformation, geometric nonlinearity and fiber orientation on axial–flexural–torsional response.