The work presented in this paper investigates the ability of continuum damage models to accurately predict matrix failure and ply splitting. Two continuum damage model approaches are implemented that use different stress–strain measures. The first approach is based on small-strain increments and the Cauchy stress, while the second approach account for large deformation kinematics through the use of the Green–Lagrange strain and the 2nd Piola–Kirchhoff stress. The investigation consists of numerical benchmarks at three different levels: (1) single element; (2) unidirectional single ply open-hole specimen and (3) open-hole composite laminate coupon. Finally, the numerically predicted failure modes are compared to experimental failure modes at the coupon level. It is shown that it is important to account for large deformation kinematics in the constitutive model, especially when predicting matrix splitting failure modes. It is also shown that continuum damage models that do not account for large deformation kinematics can easily be adapted to ensure that the damage modes and failure strength are predicted accurately.