Two-high screw rolling of billets was carried out using a MISIS-130D rolling mill. AISI 321 steel billets were deformed with feed angles of rolls of 6°, 12°, 18° and 24°. The diameter reduction was 17%, with the initial billets’ diameter being 60 mm. An axial fracture, the so-called Mannesmann effect, of the billets was observed after screw rolling. The experimental rolling was simulated using QForm finite element method software. Initial and boundary conditions were set in concordance with the experimental rolling. Several damage criteria were used for fracture prediction during computer simulation. The results of computer simulation of fracture prediction were compared with the billets fracture after screw rolling for stationary and non-stationary stages. The most effective parameter (in terms of fracture prediction) is triaxiality. The distribution of this parameter showed that the higher the feed angle value is, the lower the fracture risk is. Notably, the risk of fracture is lower at a stationary stage compared with the same risk of fracture at a non-stationary stage; the listed trends agree with experimental rolling results. The Oyane, Ayada, Brozzo, and Cockroft-Latham Normalized criteria are partly effective. These criteria are ineffective for fracture prediction 6 degrees feed angle of rolls because they showed that fracture is most probable at the billet’s surface, which contradicts the experimental rolling results. All these criteria are partly effective when predicting a less fracture risk at a stationary stage compared with the same criteria at a non-stationary stage or when predicting a decrease of fracture with increasing the rolls feed angle.