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Autofrettage is an effective technique to improve load-bearing capacity and safety for pressure vessels.For autofrettaged cylinder,the depth of plastic zone,or overstrain is a key factor which affects load-bearing capacity and safety.The previous research on overstrain was not done in terms of the point of view of raising load-beating capacity as far as possible and simultaneously avoiding compressive yield for cylinders experiencing autofrettage handling,and there were no analytic solutions of autofrettage in the above view point presented,the 3rd and 4th strength theories were not applied synthetically in the research to compare the results from these two theories.In this paper,with the aid of the analytic method,based on summing up the authors’ previous research,results from autofrettage of a cylinder based on the 3rd and 4th strength theories are studied and compared,and the laws contained in the results are looked into.Then,the essential cause and reason for the obtained laws are analyzed and the inherent and meaning relations between various parameters in autofrettage theory are revealed,It is shown that the maximum radius ratio for equivalent residual stress at inside surface never exceeds the yield strength even for a cylinder experiencing wholly yielded autofrettage,or the critical radius ratio is kc=2.218 457 489 916 7…,irrespective of the 3rd or 4th strength theories.The equation relating the depth of plastic zone with the thickness ora cylinder is identical for the 3rd and 4th strength theories.In form,the optimum load-bearing capacity of an autofrettaged cylinder is two times the initial yield pressure of the unautofrettaged cylinder irrespective of the 3rd or 4th strength theory.The revealed inherent relations betweeo various parameters and varying laws of the parameters as well as the forms of the relations under the 3rd and 4th strength theories not only have theoretical meanings but also have prospects in engineering application.