U-shaped prestressed concrete bridge decks, simply supported, are now being increasingly used in railways and highways. Simplified methods of analysis are commonly used in design practice. In the longitudinal direction, the Ugirder is modelled as a beam. However, under eccentric loading, simple beam analysis is found to yield unconservative estimates of longitudinal forces, mainly due to torsional warping. An understanding of U-girder bridge deck behaviour under torsional loading is facilitated by the application of Vlasov's thin-walled beam theory. This theory can be easily invoked as a substitute for simple beam analysis, resulting in vastly improved predictions of longitudinal stresses. The two U-girder decks have also been modelled in Structural Analysis Program software using shell elements, and the results of three-dimensional finite-element analysis validate the thin-walled beam theory. The scope of the study is limited to a straight and thin-walled U-girder bridge deck of uniform section. The effects of variation in load position have also been studied, and it is established that the thin-walled beam theory is well suited to estimate and design the U-girder for longitudinal stresses.