The problem of contact crack is common in engineering structures. Combining the advantages of numerical manifold method in crack treatment

the contact crack problem under compression and shear loads is analyzed

and the progressive propagation process of compression-shear cracks is simulated. In order to reduce errors caused by different positions of crack tips in one element

the singular cover function term is added to each physical cover near the crack tip in a certain range

and then the partitioned integration is carried out according to the position of crack tip and the number of singular physical covers in each element. A compression-shear failure example is selected to analyze the impact of normal contact force on stress intensity factor

and then the progressive failure process is simulated. The results show that the proposed method for compression-shear crack is feasible. Compared with results obtained from unrefined and refined methods

the proposed method in this paper can describe crack propagation path with much higher accuracy. The normal contact force has no contribution to mode Ⅱ stress intensity factor. However

it has great influence on mode Ⅰ stress intensity factor and the relative error varies with mesh density. Moreover

the effect of normal contact force on mode Ⅰ stress intensity factor is larger than that of inner pressure.