Hitherto, in the studies of the plastic design of steel structures, it bases on the concept of plastic hinges to determine the maximum strength of structures, or, recently in the case of high axial loaded beam-columns, the maximum load is obtained by using the method of Column Deflection Curves developed at Lehigh University. In the present paper, the finite element method is developed for large deflection and elastic-plastic analysis of frame works by using stationary potential energy of structure. Material and geometrical nonlinearlity are linearized by the incremental load procedure. This method of analysis is possibly used to determine the maximum strength of elastic-plastic frames, taking into account instability of frames and pursuing the spreading of the plastic region in each member of structures. As numerical examples, the authors calculated elastic buckling of columns with eccentric loads, beam-columns under high axial loads and moments, instability of portal frames, and sidesway failure of three-story frames. It was conclusively found that the calculated results showed a fair agreement with the experimental results.