The methods of analyzing rigid frames in present use are known to have many undesirable characteristics which are either directly or indirectly the result of limiting stress and strain to values below the proportional limit. In this investigation an analysis method is described and used that overcomes the weaknesses of the orthodox methods. The simple plastic theory is stated, explained, and used in the analysis of six rigid frames. The resulting failure loads are compared with the allowable loads of an orthodox method. Although much theoretical and experimental confirmation is required before the simple plastic theory is fully accepted, indications are that it is a very good method of approximating the failure load for rigid frames.