The simple ring frames which are a common feature of metal fuselage construction are being superseded in some large aircraft by more complicated frames in which one or more cross members are added to stiffen the frame. The stress distribution in simple rings is readily analysed by the standard methods for redundant structures, but the direct extension of these methods to more complicated cases leads normally to the solution of a number of simultaneous equations. The method now proposed avoids this difficulty by breaking down the calculation into a number of simple steps and then applying the principle of superposition to combine the results so obtained. In this respect it is equivalent to the Hardy Cross moment distribution method (1) or to Southwell's method of the systematic relaxation of constraints (2) though in many applications the final superposition of loadings is so simple that the full moment distribution or relaxation procedure is not required.