High pressure apparatus is widely used in industries, the design of them depends on stress distributions in their walls. Most of high pressure apparatuses are made in form of cylinders. To raise load-bearing capacity and extend operation life for high pressure apparatus, the autofrettage technology is often used. To design autofrettaged high pressure apparatus, it is necessary to study characteristics of stresses in the wall of thick-wall cylinders, including residual stresses and total stresses, etc. In this study, through investigating the characteristics of stresses of cylinders subjected to internal pressure according to the maximum distortion strain energy theory, a set of simplified equations for residual stresses and total stresses are obtained, the safe and optimum load-bearing conditions for autofrettaged cylinders are found out, which are the basis for design of autofrettaged high pressure apparatus.