Pressurized fluids may invade into the cement sheath of hydrocarbon wells during hydraulic fracturing and other construction operations in shale gas and oil exploitation. Excessive fluid pressure provides a driving force for small cracks to grow and tunnel through the length of the well, leading to the loss of zonal isolation and severe consequences. This work studies fluid-driven cracks tunneling in the bulk or along the interfaces of the cement sheath. We calculate the energy release rate of the tunneling crack as a function of the width of the tunnel. As long as the maximum energy release rate is below the fracture energy of the cement or the interfaces, no tunnels will form. This failsafe criterion predicts that the interfaces are much more vulnerable to tunneling cracks than the bulk of cement sheath. It is further shown that cement sheath with high Young’s modulus and high Poisson’s ratio can better resist fluid-driven cracks. The influence of casing pressure is also examined. Different loading conditions may have conflicting requirements on the properties of cement sheath. Compromises need to be made in engineering practice.