Steel thin-wall spherical vessels yield and burst strength and load will be as fuzzy variables, by using the fuzzy reliability theory, the allowable fuzzy reliability range was analyzed. The research shows that: 1)For the allowable fuzzy reliability range of the pressure vessels yield strength; in pneumatic or pneumatic-hydrostatic test, it should be not less than 0.995 52 and not greater than 0.998 54; in hydrostatic test, it should be not less than 0.979 06 and not greater than 0.983 14. 2) For the allowable fuzzy reliability range of the pressure vessels burst strength; in pneumatic or pneumatic-hydrostatic test, it should be not less than 0.999 991 52 and not greater than 0.999 999 934; in hydrostatic test, it should be not less than 0.999 79 and not greater than 0.999 984.