A boundary element method is developed for the topology optimization problem. The topological change is captured using the level set method. The level set function which is defined by signed distance from the boundary contour is assigned to fixed grid points. Boundary elements are developed along the zero contour of the level set function. The design sensitivity analysis is performed for the boundary element equation, and then the boundary velocity is obtained. The velocity field which leads the level set function to optimal material distribution is obtained by the extension of the boundary velocity. Numerical examples show that the proposed method is valid for the topology optimization problems. Copyright (c) 2006 John Wiley & Sons, Ltd.