A theory of flexure for beams with nonparallel extreme fibers is presented. The theory is shown to reduce to the ordinary theory of flexure as the angle between the extreme fibers approaches zero. Maximum fiber stresses computed by the theory and by the ordinary theory for a plate girder with nonparallel flanges show that for angles between the flanges up to twenty degrees the ordinary theory can never be in error more than about five per cent, but for larger angles the error in general increases rapidly with the angle. Finally an example is given of the application of the theory as an approximation to a beam with curved extreme fibers. In this case the theory was confirmed by the results of tests.