Abstarct: Numerical approximation for solving a differential equation has a wide range of application in engineering and mathematics. The boundary element method is a powerful tool for numerical approximation for a differential equation. In this thesis we want to approximate the Helmholtz equation by the boundary element method. This thesis organized in four sections: in the first chapter, we express disadvantages and advantages and history of the boundary element method. In the second chapter, we introduce some preliminaries and we describe the structure of the boundary element method. In the third chapter, we applied boundary element method for Laplace equation which is a special case of Helmholtz equation. Finally, in the fourth chapter we have approximated the boundary element solution of Helmholtz equation.