＜正＞Autofrettage is used to introduce advantageous residual stresses into wall of a cylinder and to even distributions of total stresses. Basic theory on autofrettage has been functioning for several decades. It is necessary to reveal profound relations between parameters in the theory. Therefore, based on the 3rd strength theory,σej/σy,σei/σy,σej′/σy,σei′/σy and their relations, as well as p/σy,are studied under ideal conditions, whereσej/σy is equivalent stress of total stresses at elastoplastic juncture/yield strength,σei/σy is equivalent stress of total stresses at inside surface/yield strength,σej′/σy is equivalent stress of residual stresses at elastoplastic juncture/yield strength,σei′/σy is equivalent stress of residual stresses at inside surface/yield strength, p/σy is load-bearing capacity of an autofrettaged cylinder/yield strength. Theoretical study on the parameters results in noticeable results and laws. The main idea is:to satisfy |σei′=σy,the relation between kj and k is k~2 ln kj~2-k~2-Kj~2+2=0, where k is outside/inside radius ratio of a cylinder,kj is ratio of elastoplastic juncture radius to inside radius of a cylinder;when the plastic region covers the whole wall of a cylinder, for compressive yield not to occur after removing autofrettage pressure, the ultimate k is k=2.218 46,with k=2.218 46, a cylinder’s ultimate loed-bearing capacity equals its entire yield pressure,or p/σy=（k~2-1）/k~2=lnk; when kj≤e1/2 =1.648 72, no matter how great k is, compressive yield never occurs after removing p,;the maximum and optimum load-bearing capacity of an autofrettaged cylinder is just two times the loading which an unautofrettaged cylinder can bear elastically, or p/σy =（k~2-1）/k~2, thus the limit of the load-bearing capacity of an autofrettaged cylinder is also just 2 times that of an unautofrettaged cylinder.
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