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Braided composites are widely used in engineering, but there is little research on the bimodulus constitutive relation of tension and compression. In this paper, a bimodulus constitutive model suitable for two-dimensional (2D) 2 × 2 braided carbon fibre composites is proposed. The modulus prediction method and stress rotation formula were optimised and verified. According to the tension and compression tests and two stacking sequences that were conducted, the degrees of deviation of the moduli were found. To identify the underlying cause of the modulus deviation, two unit cell models were built with different stacking angles. By changing the fibre volume fraction and braiding angle of the unit cell models, the tensile and compressive moduli under the influence of these two parameters were obtained. As the fibre volume fraction and braiding angle increased, the deviation degree of the two moduli increased. When the braiding angle was small, the tensile modulus was greater than the compressive modulus, while when the braiding angle was relatively large, the compressive modulus was greater than the tensile modulus.