In this paper the non-linear theory of thin 一 walled beams of open cross sections Proposed by the author [1] recently is applied to the investigation of the stability of such beams. Fundamental equations of the previous paper [ 1 ] are firstly linearized and simplified for the determination of the critieal load and the mode of buckling.In the ease of eccentrie compression, the fundamental equations of this paper differ from those in the theory of V.Z.Vlasov in the following two points : l) A new generalized displacement P is in troduced.2 ) The initial bent state of the beam is taken in to account. A numerieal exaple (an angle of unequal legs ) shows that in the case of central uniform compression, P has little in fluence on the magnitude of the critical load, The re fore P is then neglected in this paper.In the ease of beams loaded by pure bending momments , two numerical examples are carried out (a cross beam and an I-beam , see Figs.4 and 6 ). Critieal moments are ploted against a d imensionless parameter a as shown in Figs.5 and 7(curves I), where a is the ratio of width to depth of the cross section of the beam·Our critical moments are greater than those given by V.Z. Vlasov (curves II in Figs.5 and 7).This is because in this paper the initial bent state of the beam is taken into : account. It is interest to point out that according to our theory, beams may lose lateral stability under pure bending moment only when the ratio of width to depth of the cross section is less than a certain critical value. This fact is in agreement with common exprience .