Development of solution strategy for tracing simultaneously plastic collapse and buckling behavior of the plane framed structure is essential. In this pa야r a numerical finite element procedure which can consider plastic hinge and find geometric non-linear equilibrium path of arbitrary plane frame structures is presented. The member is assumed to be prismatic and straight, and has the rectangular cross section. The limit state condition of the plastic hinge is derived under the combined condition of a bending moment and a axial force. Two cases of elasto-plastic stiffness matrices derived from different assumptions are presented. Numerical examples are presented in order to demonstrate the validity of the proposed procedure.