Abstract: It is indicated by macroscopical and microscopicalexperiments that most of the directions of failure particle pair are notconsistent with the direction of the first principal stress. Accordingto the microscopicmechanics with respect to brittle materials' tensile failure, the material willbegin to decompose if the distance between pair particles exceeds theirattraction distance. Based on the above facts, a new strength criterion ofbrittle materials' tensile failure is derived, which can be written as:\sigma_1+\alpha \sigma_2+\beta \sigma_3\le \sigma,in which the coefficients are dependent on the predominant angle andPoisson's ratio. It is pointed out that the reason why the classical criteriadisagree with experiments is that the predominant angle is not considered inthe classical criteria. The new criterion is shown to be more accuratethan the classicalcriteria for tensile failure of brittle materials by experiments.