The 2D/3D numerical simulations of the Brazilian tensile test were carried out by using continuum elasto-plastic analysis to reveal the variation of the fracture modes of Brazilian disks and its fracture evolution processes. The influence of the compression-tension ratios and contact loading angles on the fracture modes of the disc specimens is studied through the 2D simulations and through the 3D simulations, the initiation and expansion processes of the 3D fracture is explored. The research results show that the larger the contact loading angles and the compression-tension ratios, the more likely the Brazilian disc specimens to crack firstly at the disk center; the fracture initiation under the loading rims is caused by shear failure but the further propagation of the split fracture is driven by tension failure. The results of the 3D numerical simulations show that the initial crack initiation point is always located on the end face of the disc, and it gradually moves to the center from the load-end as the loading angle increases; when the central tensile cracking appears, the 3D fracture surface expaned toward the inside of the specimen with an arc boundary. Regardless of whether the disc specimen starts to fracture initially at the disk center or at the loading point, the Brazilian tensile test may underestimate the tensile strength of rocks due to the 3D effect.