As one of the fault-related instability problems of tunnels, rock slip along fault plane is closely related to the shear strength of a fault, and usually causes irrecoverable and sometimes catastrophic engineering problems. In this paper, based on continuum assumption and Coulomb-slip failure, a criterion to evaluate rock slip along the fault plane was proposed for a circular tunnel in rock masses containing a fault. A mathematical equation that describes the relationship between required shear strength of a fault and horizontal stress ratio, fault spatial extension and location was established. From the equation, the influences of the important parameters on the required shear strength of a fault was analysed after a numerical validation was performed. Besides, the effects of fault spatial extension and location on the tunnelling-induced shear displacements were characterized through numerical models. Characteristics of the tunnelling-induced shear displacements at the excavation wall indicated that fault location with respect to the tunnel dominates the nonuniform rock deformations at excavation wall, and larger fault dip angles could lead to larger shear displacements in some specific pair cases. The presented investigation provides both a deeper insight into the instability problems of tunnels related to a fault and a guideline for tunnel support design.