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The propagation of the interfacial cracks at Cu/SiC interface under tensile (mode I) loadings and combination of tensile and shear (mixed mode) loadings are studied by molecular dynamics (MD) simulations. For the mode I, the asymmetrical interfacial crack propagation is observed at the interface, and the stress concentration is found both at the crack tip and somewhere of interface due to the lattice mismatch. Six loading methods with different loading angles are considered in this work, the behaviors of the crack propagation are found to be dependent on the loading angles. In addition, the Rice and Thomson (R–T) model is also used to predict the behaviors of interfacial crack growth theoretically. With pure tensile loading, the energies necessary for dislocation nucleation at the two crack tips are found to be different, which leads to asymmetrical crack propagation. For the mixed modes, the behaviors of the crack propagation are predicted by comparing the dislocation nucleation energy and the decohesion energy. The predictions of the R–T model are consistent with the MD results qualitatively. This research is intended to provide a fundamental explanation of the asymmetrical crack propagation at interface from atomscale.