Numerical simulations of a naturally fractured shale reservoir are used to investigate the influence of sequential hydraulic fractures on the shear displacements and evolving stability of a fault. The effect of the heterogeneous elastic strains arising from natural fractures and faults in the reservoir on the displacements around hydraulic fractures is simulated. The displacements experienced by the hydraulic fractures depart strongly from the elliptical distribution characteristic of homogeneous elastic media, and are a result of the influence of natural fractures and faults by both superposition of elastic strains and inelastic behaviour. It is shown that interaction between the pre-existing reservoir strains and those induced by hydraulic fracturing influence shear displacements along the fault. Displacements on the fault respond to the hydrofracture-induced shear strains, tend to be restricted to certain patches of the fault and mainly tend to stabilize the fault. The results imply that the numerous closely spaced hydraulic fractures characteristic of current shale reservoir completion practice may, to some extent, increase the stability of potentially unstable faults before they are intersected by a propagating hydraulic fracture. The stability of the fault as the fractures sequentially approach the fault depends upon the direction of approach and the dimensions of the hydraulic fractures.