Carbon/epoxy composites demonstrate significant promising improvements of weight to performance in the automotive industry. However, the design of carbon/epoxy composite components for crashworthiness remains challenging and normally requires laborious and repeated experimental work. This study adopts a predictive crush model of carbon/epoxy composites, which can partially replace the experimental work. The discontinuous Galerkin (DG) method with extrinsic cohesive laws is employed to simulate the failure patterns in the composite structures. The application of DG distinguishes the fracture model from the conventional approach where preset cohesive elements are used on the location where cracks are expected. The mixed mode cohesive laws are used to simulate the delamination between each layer. To capture different crack propagations in different layups, the anisotropic cohesive law is used to simulate the intralaminar crack propagation in composites. To verify the adopted model, circular composite tube specimens with different layups have been simulated and compared with tests under quasi-static crush loadings. The comparisons of numerical results with experimental data show that the DG crush model can reproduce the experimental results with relatively high accuracy.