Abstract: Rock materials commonly exhibit tension-compression bi-modulus behavior, which has a crucial influence on the determination of tensile strength in the Brazilian test but is often neglected in traditional analyses. To systematically investigate the effects of this property on the elastic modulus and stress distribution in Brazilian discs, a stress-driven bi-modulus numerical model is developed. The mechanical behavior of the Brazilian disc under different compression-to-tension modulus ratios is studied, and the calculation differences between the transversely isotropic model and the bi-modulus model are compared. The influence of tension-compression bi-modulus characteristics on tensile strength is analyzed, and a new calculation formula is proposed. The results indicate that: (1) Tension-compression bi-modulus characteristics significantly affect the elastic modulus and stress distribution in the Brazilian disc, especially under high compression-to-tension modulus ratios; (2) The stress and strain calculation results in the vertical direction are consistent between the transversely isotropic model and bi-modulus model, but there are significant differences in the horizontal direction; (3) The traditional tensile strength calculation formula based on isotropic assumptions overestimates rock strength, with the relative error increasing as the compression-to-tension modulus ratio increases, reaching up to 54.95%; (4) The proposed formula accurately describes the horizontal stress at the disc center, with relative errors below 5%. It effectively mitigates strength estimation errors caused by neglecting the difference between tensile and compressive moduli, thereby providing a reliable method for determining the tensile strength of bi-modulus rocks.