The Rayleigh-Ritz method is a convenient tool for the analysis of deflections in structures subjected to external forces. Bending moment relations can be developed and reliable values obtained for bending moments. In this thesis the Rayleigh-Ritz method is used for the analysis of a single-span, pin-connected circular arch subjected to uniform load along the arch. The method is explained, equations for deflections and moments are developed and the results of an illustrated problem are tabulated. The illustrated problem is also solved by a conventional method using the dummy load and virtual work techniques. Results are compared and found to be good. In both methods, account is taken of bending and axial forces; shear distortion is neglected. For the Rayleigh-Ritz method where undetermined coefficients are evaluated, a tabulation of the rate of convergence is presented. Computer programs for both methods are included. / Master of Science