According to the basic theory on autofrettage and according to the 4th strength theory, several parameters and their relations are studied under ideal condition,includingσ_(ej)/σ_y,the equivalent stress of total stresses at elastoplastic juncture;σ_(ei)/σ_y,the equivalent stress of total stresses at inside surface;σ_(ej′)/σ_y,the equivalent stress of residual stresses at elastoplastic juncture;σ_(ei′)/σ_y,the equivalent stress of residual stresses at inside surface;and p/σ_y,load-bearing capacity of an autofrettaged cylinder.By theoretical study on relations between the parameters,noticeable results and laws are achieved:to satisfy|σ_(ei′)|=σ_y,the relation between k_j and k is,k~2lnk_j~2-k~2-k_j~2+2=0,when k→∞,k_j=e~(1/2)=1.648 72,as based on the 3rd strength theory,where k is the outside/inside radius ratio of a cylinder,k_j is the ratio of elastoplastic juncture radius to inside radius of a cylinder;If 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 as based on the 3rd strength theory;With k=2.218 46, a cylinder’s ultimate load-bearing capacity equals its entire yield pressure,or p/σ_y=2lnk/3~(1/2);The maximum and optimum load-bearing capacity of an autofrettaged cylinder is just 2 times the loading which an unautofrettaged cylinder can bear elastically,or p/σ_y=2(k~2-1)/3~(1/2)k~2,and the limit of the load-bearing capacity of an autofrettaged cylinder is also just 2 times that of an unautofrettaged cylinder.The conclusions are the same as based on the 3rd strength theory,but some equations are different from each other. According to the basic theory on autofrettage and according to the 4th strength theory, several parameters and their relations are studied under the ideal condition, including σ_ (ej) / σ_y, the equivalent stress of total stresses at elastoplastic juncture; σ_ (ei) / σ_y, the equivalent stress of residual stresses at inside surface; and σ / σ_y, the equivalent stress of residual stresses at elastoplastic juncture; σ_ (ei ’) / σ_y, the equivalent stress of residual stresses at inside surface; , load-bearing capacity of an autofrettaged cylinder.By the theory of relations between the parameters, noticeable results and laws are achieved: to satisfy | σ_ (ei ’) | = σ_y, the relation between k_j and k is, k ~ 2lnk_j ~ When k → ∞, k_j = e ~ (1/2) = 1.648 72, as based on the 3rd strength theory, where k is the outside / inside radius ratio of 2 - k ~ 2 ~ k_j ~ 2 + 2 = 0 a cylinder, k_j is the ratio of elastoplastic juncture radius to inside radius of a cylinder; If the plastic region covers the whole wall of a cylinder, for c omp’s occur 2 lnk / 3 ~ (1/2); The maximum and optimum load-bearing capacity of an autofrettage cylinder is just 2 times the loading which an unautofrettaged cylinder can bear elastically, or p / σ_y = 2 (k ~ 2-1) / 3 ~ (1/2) k ~ 2, and the limit of the load-bearing capacity of an autofrettaged cylinder is also just 2 times that of an unautofrettaged cylinder. Theses are the same as based on the 3rd strength theory, but some equations are different from each other.