This paper investigates the effects of the microstructure of a composite material (including fibre volume fraction, fibre distribution and bonding quality between fibre and matrix) on normalized maximum principal stress under transverse tension and shear of a unidirectional carbon fibre reinforced composite. The normalized maximum principal stress is defined as the stress ratio of maximum principal stress to the load applied. A Finite Element (FE) model using a concept unit cell with different composite characteristics subjected to transverse tension and shear has been developed to enable an understanding of microscopic damage mechanisms and failure behavior for carbon/epoxy composites. This information, which has been verified against physical test results, is vital to instruct the composite manufacturing process and part design criteria.