The formation of major strike-slip faults remains enigmatic in the framework of plate tectonics. Using 3D finite element models, we show that the co-existence of extension and shortening (at a high angle with the extension direction) and a weak lithosphere (e.g high geotherm) can trigger normal faulting and strike-slip faulting. Our results are compared to the Aegean example where strike slip faults (e.g. North Anatolian fault) and normal faults (e.g. Corinth rift) work together.