In the present study, the buckling behavior of beams is analyzed by a plane strain finite element. The displacement-type finite element formulation is based on elasticity and has no any other simplification and assumption except that the beam is of moderate depth. Also all the displacement boundary conditions can be imposed exactly. These are the advantages that beam theories of conventional approach, which simulate beams with neutral plane behaviors, do not have. Therefore the present analyses should be able to obtain buckling load and buckling mode more accurately than conventional method. Numerical values of buckling loads of the present approach will be compared with previously published results of the Euler-Bernoulli beam theory and the Timoshenko beam theory, and further with the high order beam theory to reveal their differences. The effects of the geometry ratio, the distribution of axial loads and the displacement boundary conditions on buckling of beams are also discussed.