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This paper extends the theory of interval arithmetic and applies interval analysis in software static analysis. It defines the concept of interval-set on numeric variables and its operations, introduces the interval computations on Boolean and reference types, and gives the possible value set and necessary value set of a variable in the condition expression. It also presents an approach of static analysis based on interval analysis (SABIA). Our experiment results show that SABIA can directly detect a certain number of infeasible paths in program, and the testing tool DTS_Java based on the approach can eliminate false positives efficiently.