The purpose of this thesis has been achieved. Vector notation has been used in developing the equations necessary for the analysis of three dimensional elastic rings. An elastic centroid for the elastic ring has been located with a tabular procedure for exacting the solution to the problem. For a comparison of the solutions between the method based on three elastic centroids with the method based on one elastic centroid, one need refer to Figures 7 and 10. Comparing the two methods, it is the author's opinion that the method herein presented is superior if for no other reason than simplicity. The development of the six equations can be readily followed and the tabular form of Figure 7 presented as an orderly means for obtaining the coefficients of the six unknowns. Figure 10 presents a method involving a similar tabular form as in Figure 7 along with the additional calculations that must be made before the correction moments and shears can be obtained. The necessity of these additional terms serves to obscure the physical significance of the final equations. / Master of Science