The materials with different elastic behavior under tension and compression are called bi-modulus materials, and this type of materials widely exists in nature, such as rock, concrete, and cohesive soil. However, due to the lack of a constitutive model that is suitable for bi-modulus materials, the bi-modulus property of materials was often ignored in previous studies. In this study, the uncoupled strain-driven constitutive model for bi-modulus materials proposed by Latorre and Montáns1 is firstly embedded into the finite element software FssiCAS. Then the distribution characteristics of stress, strain, and displacement in Brazilian disc are systematically compared under the two conditions, i.e., considering the bi-modulus property and ignoring them. Besides, the constitutive model is used to verify the reliability of the measurement methods proposed by Ye et al.2,3 for the tensile elastic modulus. The results show that the bi-modulus property of materials has a significant effect on the magnitude, and the distribution of stress, strain, and displacement in Brazilian disc. The measurement methods proposed by Ye et al.2,3 own acceptable reliability only under certain conditions.