Abstract: The uncertainty in the flaw size determination and the flaw detection has been studied,and a fuzzy theory of nondestructive testing (NDT) is established.The mathematical relations between the measured flaw sizes by NDT and the actual flaw sizes is presented.The distribution of true flaw sizes is obtained at a given measured flaw size.Fuzzy interval evaluation and membership degree of the flaws exceeding the specified size are given.Thus a quantitative method for determining the actual flaw size is successfully developed to make full use of the measured flaw sizes from different NDT sources.The new concepts of fuzzy life estimation,fuzzy fracture criterions,fuzzy damage tolerance design,fuzzy assessment of the pressure vessel integrity should be put forward on the basis of the fuzzy theory of NDT.