Abstract: The radiation theory of piston transducer in an infinite rigid plane baffle is not accurate to characterize the beam pattern of unbaffled circular piston transducer for ka<π.A simple mathematical modeling method based on the union of Finite Element Method(FEM) and curve fitting technique has been developed to solve this problem.Two modifying factors are introduced into the basic function expression of classical theory at first.Then the precise mathematical expressions of them are obtained through curve fitting method by numerical simulation.Thus the whole empirical formula model for beam pattern of unbaffled circular piston transducer is built.The results of this model agree well with the FEM solutions for ka in the range from 0.03 to 5.2.Furthermore,the model is identical with classical theory for greater ka.