Abstract: This paper analyses the buckling of top-outrigger-braced frame-tube structures. By analyzing a simplified model of an outrigger-braced structure, the contributions of component rigidities of the outrigger to the stability of the overall structures are identified. The buckling of top-outrigger braced structures is analyzed using a continuous model, and a simple formula for the buckling load of the structure is proposed. Compared with accurate solution, the proposed formula shows good accuracy. Second order analysis is carried out for three types of lateral loads, with the concentrated vertical load acting at the top of the structure, the amplification factors for the lateral displacement and moments of various members are derived and an approximate equation with good accuracy is presented.