Abstract: The fractal finite element method is extended to solveexterior acoustic problems. An artificial boundary is introduced to dividethe exterior domain into two parts. The conventional finite element methodis adopted within the artificial boundary, and the fractal finite elementmethod is employed in the outer region beyond the artificial boundary.Because of the facts that the relationships of element matrices between theadjacent fractal layers are very simple and the node degrees of freedom aretransformed into a set of general coordinates by using the globalinterpolation functions, which satisfy automatically Sommerfeld's radiationconditions, the computer time can be reduced greatly by the fractal finiteelement method. The numerical results show that this method is effective insolving exterior acoustic problems.