A method is presented for predicting the effect of a local modification such as the addition or removal of a concentrated mass or linear spring on the vibration characteristics of a linear system. The method, which is mathematically applicable to any linear eigenvalue problem, is rigorous even for large changes and has its basis in an eigenfunction expansion of the solution of the modified system in terms of the eigenfunctions of the unmodified system. Given the natural frequencies and modes of the original system, the characteristic function of the modified system is of such a form that it may be solved with a significant reduction in work as compared with direct treatment of the new system.