The location of the failure initiation in the Brazilian test is strongly influenced by the contact angle created in the loaded area. As this angle increases, the position of the initial failure point is closer to the center of the disc, which is a result of both: uniform radial pressure and sinusoidal radial pressure; as well as adopting different failure criteria and materials. Moreover, the frictional stresses throughout the contact between the jaw (or platens) and the disc cannot be considered as a critical failure parameter for failures initiated from the origin to a radial distance of 0.8R.In this paper, firstly, the influence of the above mentioned parameters in the location of the initial failure point was analytically studied. Secondly, the analytical results have been proven through experimental tests. Finally, once the importance of the contact angle in the location of the initiation point was checked, a procedure is suggested in order to increase the contact angle with the same load applied to one specific sample, by using various jaw curvatures.The location of failure initiation does not cause great disturbances in the determination of the indirect tensile strength. However, the position is important in order to adjust the failure criteria in the tension region. According to the location of the initial failure, the stress field in terms of principal stresses (σ1 and σ3) will be different. So by knowing this position, the precise failure criteria could be established in σ1 - σ3, specifically in the tension region. Meaning that as well as the triaxial test is mostly used to calculate the failure criteria in the compression region, the Brazilian test could be used to obtain the limiting stress states in the tension region.