The problem of cut-outs in structures being analysed by the matrix force method is solved by Goodey by the method of undetermined multipliers. It can be shown that the final results are identical to those of ref. 2. In this note we demonstrate that the method of undetermined multipliers can also be used to incorporate modifications into a structure. This, in itself, is only of academic interest for a simple problem. However, it does give many advantages when dealing with more complex situations. The basic equations can be written down quite simply and the development of the subsequent matrix algebra follows the straightforward pattern for solving simultaneous equations. Also, where previous results can be used, this becomes apparent.