The formation mechanisms for layer interface-parallel discontinuities and their interactions with vertical cracks in layered rocks with varying layer thickness are investigated. The interface behaviour between rock layers is modeled by a shear displacement response and rock crack behaviour is described by a damage model. Three typical failures can be captured: (1) vertical cracking, (2) delamination and (3) interface-parallel cracking. The result further indicates these crack modes are determined by a threshold of the interfacial strength. When the interfacial strength is higher than the threshold, a combined pattern of vertical cracking and interface-parallel cracking occurs. If the strength is lower than the threshold, a combined pattern of vertical cracking and interfacial delamination can be found. If the strength for the interface is near the threshold, a combined pattern of interface-parallel cracking, vertical cracking and interfacial delamination occurs. The result shows the interface-parallel discontinuities are induced by interface-delamination, interface-parallel cracks, or their coupling behaviour. Both interfacial delamination and interface-parallel cracking can reduce the tensile stress between two adjacent cracks and thus lead to a saturation state. Layer thickness variations can further influence the infilling process of vertical cracks and the crack spacing to average layer thickness ratios.