Prestressed concrete double tees are sometimes set on non-parallel supports to facilitate drainage; this practice induces twisting in the members. If the twist angle is large enough, cracks may occur in the flanges adjacent to the web-flange junction. This paper identifies the important modes of deformation and presents an analysis of the stresses and deformations caused by twisting. Local distortions of the cross section near the member ends are shown to play a pivotal role in bending and cracking of the flanges of double tees. A new theory of torsion that includes those deformations is developed, and a parametric study is carried out to show the effect of variations in the dimensions of the member. Finally, based on the new theory, the paper presents several graphs that facilitate the computation of the twist angle that causes cracking in a double tee of common dimensions.