Prestressed concrete girderless roof under solar radiation and seasonal temperature difference is likely to crack．In order to study the mechanism of cracking，two finite element analysis models of the roof were developed with the finite element software ABAQUS．Their stress distribution nephograms were obtained．The results show that this kind of roof generally cracks near the fascias under solar radiation，and the cracking direction is parallel to the edge of the fascias or is perpendicular to the diagonal line of the fascias，while under seasonal temperature difference，the roof generally cracks near the post-pouring strip，and the cracking direction is parallel to the edge of the fascias and the cracks may be penetrating．