Abstract: This paper consists of four parts:(1)According to the Griffith theory of brittle strength the formulae of a criterion of failure were derived by author under the stress field (convention is that the tensile stress is positive) and applied them to analysis of the natural crack for reservoir; (2)Three numerical models and computative method of the quantitative analysis for paleo-stress as well as a method of the quantitative prediction for paleo-naturil crack were given in the reservoir of the carbonate rock; (3)A concept of effect tensile stress was presented a description of the natural tensile crack was provide for reservoir; (4)To provide a predicted tensile crack distribution map for reservoir of the carbonate rock and test it through drilling holes.