Acoustic design sensitivity formulations presented in this paper are obtained by differentiating the boundary integral equations with respect to design variables.They are employed to calculate the rates of change of response quantities associated with an object with respect to changes in the design variables that determine the shape of the given structure.Zheng et a1.[1,2,3] employed the fast multipole boundary element method to three dimensional acoustic design sensitivity analysis and derived two different formulations by using direct differentiation method and adjacent variable method.The conventional boundary element method (CBEM) for acoustic problems has nonunique solution at a set of fictitious eigenfrequencies.The effective alternative to overcome this problem is the Burton-Miller method [5] which consists of a linear combination of the conventional boundary integral equation (CBIE) and its normal derivative equation (NDBIE).It is well-known that the hypersingular boundary integral equation will be obtained when the Burton-Miller method is used.The strongly singular and hypersingular integrals in the sensitivity equations can be evaluated explicitly and directly with Hadamard finite part integral method when constant elements are employed to discretize the boundary.The BEM discretizes the boundary instead of the domain and takes less CPU time due to the one-dimension reduction in mesh generations.But the BEM produces a dense and non-symmetrical coefficient matrix.It needs O(N3) arithmetic operations to solve the BEM system of equations directly, such as by Gauss elimination method.And the size of memory of storing coefficient matrix generated by BEM is O(N2) as for a problem involving N degrees of freedom.Obviously, acoustic design sensitivity analysis will take much more time than acoustic state analysis.So the above drawback has limited the extensive usage of the BEM in large-scale engineering applications.The fast multipole method (FMM) can be used to accelerate the solution of the BEM system of equations and decrease memory requirement to O(N).