Abstract: The buckling and post-buckling analyses of carbon fiber reinforced epoxy-matrix composite (CFRP) arm under compressive and torsional loading conditions were addressed based on three-dimensional Puck failure criterion and phenomenological modulus degradation method. Taking into account the in-situ effect of the laminated structure and the effect of stress along the fiber direction on the transverse strength, a buckling analysis method considering progressive failure process of CFRP structures was established. The numerical implementation was realized by ANSYS material subroutine USERMAT. It is verified by comparing with the experimental results in the literature that, the new method can analyze the progressive failure process and post-buckling behavior of the composite structures with high accuracy. Furthermore, this method was used to analyze the buckling load and post-buckling behavior of a spacecraft composite arm under compressive and torsional loads.