The search for a better method of analyzing skew arches and rigid frames has gone on for years. During that time many theories were presented, most of which were an improvement or a simplification of previous methods. However, no exact analytical solution, based on classical plate theory, for the analysis of skewed plates as found in rigid-frame bridges had been developed prior to this thesis. As previously mentioned, the complete solution is being presented in three separate theses. This thesis contains all the equations needed for the analysis that arise from considering the extensional forces acting in the skewed slab. All the equations have been given in the form of an infinite series. These equations, together with the ones for the other parts of this problem, must be expanded for a few terms, combined and solved. Due to the size and number of equations involved, the only practical solution would involve the use of a modern high-speed computer. Since Virginia Polytechnic Institute has a computer of this type, the entire analysis could he completed at the college. Once the results are obtained, a comparison can be made with the experimental analysis referred to in the thesis. / Master of Science