Abstract: Based on the Guyan reduction and epsilon algorithm, an adaptive iteration method for structural static reanalysis of topological modification is presented. In this process, the equations of the newly added degree of freedoms (DOFS) (if any) are condensed to the original structure by means of Guyan reduction. And then, the basis vector is formed using Neumann serial according to the increment of the stiffness matrix, and the epsilon algorithm is used to accelerate the convergence of the partial sum of the basis vectors. An error evaluation method is introduced to control the accuracy of the iteration adaptively. A numerical example is given to compare the computational cost and approximation accuracy between the combined approximation and the presented method, the numerical results show that the present method is effective and easy to integrate into a general optimization approach.