As study on the burst pressure probability distribution of single-layer cylindrical vessels is a basic work,the establishment of pressure vessels reliability design method was carried out to build precision evaluation system of pressure vessel strength calculating formula. The burst pressure probability distribution of single-layer cylindrical vessel was analyzed by using the hypothesis test method in the mathematical statistics theory,based on 84 sets measured burst pressure data of single-layer cylindrical vessel. Research results indicated that:（ 1） Based on the engineering practice of Chinese standard,the application range of the formula can be divided into the 3 groups according to the design pressure which are no exceeding 35 MPa,between35 MPa and 100 MPa,and no more than 100 MPa,respectively;（ 2） According to the relationship between design pressure and burst pressure,the actual burst pressure of the formula application range sample was no more than 105. 5 MPa,between 91. 0 MPa and 329. 6 MPa,and no more than 329. 6 MPa,respectively;（ 3） When the significance was 0. 05,the ratio of the samples measured burst pressure and mid-diameter formula and Tresca formula calculated values is 6 random variables with the normal distribution.（ 4） When the 2-sides confidence was 98%,the distribution parameters value range of 6 random variables were obtained respectively.