Abstract: Most mechnical vibration of machine is a random process of obvious randomness.The common boundary element method can not calculate the problem about the structural sound radiation with random boundary condition. In this paper, a statistic boundary element method is developed that combines the statistic method with the common boundary element method,and thus obtained a calculating formula to solve the sound field radiating by a structure with random vibration. Through an example solved the random sound field, it has been proved that the method is correct.