A new method to simulate the varying static receptance of a thin-walled workpiece based on the Cholesky decomposition is presented in this paper. In this method, the system stiffness matrix is updated by subtracting the elemental stiffness matrices of the removed elements from the initial system stiffness matrix. The updated system stiffness matrix is permuted by using a novel method based on element removing sequence and considering fill-in reduction. The Cholesky factor of the permuted system stiffness matrix is reused to compute the static receptance of the workpiece for multiple cutter locations. The reduction of computation time by using this new method is proved by a numerical test and the accuracy of the simulation is demonstrated with a machining test.