Using a finite element technique, a computer program is developed which can find the elastic and the elasto-plastic lateraltorsional buckling loads for simply supported beams. The program is such that the beam, uniform in cross-section, may be loaded in any general manner and restrained at any number of points by elastic or rigid restraints. In addition, further practical considerations, such as residual stresses and non-centroidal loading, may be included in the analysis. In the program, the analytical method is based upon a known finite element stiffness analysis applicable to simple elastic problems. In the extension to general elastic problems, an improved element is proposed which considers the variation of the loads over the length of the element. The method is adapted to elasto-plastic problems by considering the effect of the yielded m.aterial on the total element stiffness, and hence on the overall beam stability. Although the effect of many practical considerations have been incorporated in the analysis, the program retains a simplicity of application through the use of simple data statements pertaining to each parameter.Results are obtained for known classical problems which illustrate the high degree of accuracy achieved with the analysis. General sample problems are examined to show the versatility of the program and ttie effect of various parameters on beam stability. Finally, a comparison of a computed solution with the results from an experimental problem illustrates the accuracy and value of the program in dealing with general practical problems. A literature survey is included together with a list of references. In addition, the entire listing of the program, a comprehensive flow chart, and a program user's guide are given in the appendix.