In the previous paper the buckling of a stiffened panel with a symmetric type of stiffener was treated as an eigenvalue problem of an orthotropic plate with proper moduli of materials in the strainhardening range. The equation of echuilibrium of a stiffener can be generalized for an arbitrary shape of thin-walled open cross-section attached to a plate if proper consideration is given to the mutual interaction between plate and stiffener.V if a beam with an arbitrary cross-section is subjected to transverse load, the beam is bent and twisted simultaneously unless the line of loading passes through the shear center. When a beam is attached to a plate, the enforced axis causes twisting of the stiffener if it is bent or the other way around, bending of the stiffener if it is twisted. Therefore the bending and the twisting of the stiffener are no longer separable for such a stiffener with an unsymmetric cross-section. When the plate starts to buckle, the distributed resistance due to the longitudinal and or transverse stiffener can be obtained from the equation of equilibrium of a stiffener attached to the plate. The integral equation for the buckling of a longitudinally and transversely stiffened plate can be formulated as in the previous paper. The buckling strength of a stiffened plate is obtained as an eigenvalue of the integral equation. From the computation given in this paper it may be concluded that a longitudinal stiffener is tolerably effective to prevent the buckling of a plate compared to a transverse stiffener, and the efficiency of an inverted angle stiffener is considerably lower than that of a Tee stiffener when the stiffener is subjected to axial loads as in a longitudinal stiffener. In other words, the existence of axial load weakens the torsional resistance of a stiffener with an unsymmetric open cross-section as well as the bending resistance of the stiffener, and its influence for an unsymmetric cross-section is considerably greater that for a symmetric one. The results of this paper, together with the previous one, are used to specify the proper geometric conditions of the siffened plate such that each panel may develop large plastic deformation without buckling and a consequent fall-off in load. These requirements are essential for a successful application of Plastic Design Methods to plate structures.