The local buckling of tubular members after ultimate strength is attained was investigated from both experimental and theoretical viewpoints. First, axial compression tests were carried out on three tubular specimens similar to the bracing member in an existing semisubmersible drilling unit. It was known that : (1) After the ultimate strength was attained, local buckling of a cosine mode first takes place at the compression side of bending. The buckling wave spreads about one half circle in the circumferential direction, but has short wave length in the axial direction. (2) At the same time, load carrying capacity suddenly decreases. (3) Then, the formations of local denting deformation follow at the foot of initial cosine buckling wave. A simplified method was proposed to analyze the elastic-plastic behaviour of a tubular member under axial compression. Two models were newly proposed which simulate the post-local buckling behaviour of a tubular member based on the observed results in the experiments. They are COS model and DENT model. Combining these models with the proposed simplified method, a series of analysis was performed on the test specimens newly carried out and previously done. The results of calculations were compared with the experimental ones, and the validity and the usefulness of the proposed method of analysis were demonstrated.