Abstract: To explore the advanced analysis approach of three-dimensional structures, an incremental virtual work equation for the stringent three-dimensional element is proposed based on the UL method. The stringent geometric nonlinear tangent stiffness matrix for three-dimensional beam-column element is derived in detail using interpolation functions cosidering shear effects. The dual nonlinear incremental stiffness equation is deduced besed on the proposed simplified plastic zone model for three-dimensional beam-column element. A dual nonlinear analysis computer program for space steel frame structures is developed. Numerical examples including both geometric and material nonlinearites are used to demonstrate the robustness, accuracy and efficiency of the proposed analytical method and the computer program. The developed computer program can be used to predict accurately the utmost resistance capability and instability mode of three-dimensional columns and space frames by modelling each physical member as one element in most cases.