Composite beams are the beams made of steel and concrete. Since 40s, with the advent of the composite beams criteria, in AASHTO standards, there has been a growing trend toward using these beams. In composite beams, mass, resistance against corrosion and fire are provided by concrete and ductility and tensile strength are provided by steel. In the present study, with the contribution of finite elements method and by using elements with 30 degrees of freedom and regarding the thin plates hypotheses, local and distortional buckling are investigated. In order to extract the stiffness matrices, the principle of minimum potential energy is used. Both local and distortional buckling of theses beams are investigated in elastic mode. For the local buckling, width to web thickness of web ratio and the width to flange thickness ratio, are investigated and they are mostly inversely proportional to the critical stress. Moreover, for the distortional buckling, the width to web thickness ratio and the width to flange thickness ratio are examined and as a result, they are generally inversely proportional to the critical load.