Fluid injection at a pressure below the local minimum principal total stress in a fault may (re)activate shear crack propagation (hydroshearing). Because of the presence of asperities along the fault's surfaces, fault hydraulic width increase with slip. Scaled experiments in fact show that dilatancy (inelastic increment of hydraulic width) varies non linearly with the slip up to a constant value (for large values of shear displacements) [3]. Its effect on pore pressure diffusion along the fault is a local drop at the crack tip. Depending on the ability of the fluid to flow in the newly created void space, the local effective stresses increase and this leads to a stabilizing effect [2]. The questions we want to address in this contribution are the fol- lowing: does the increment of hydraulic width (dilatancy) always kill the dynamic instability associated with a frictional weakening fault subjected to fluid injection? does the change of fault permeability associated with dilatant hardening affect the shear crack propagation? Garagash & Germanovich [1] showed that the regime of propagation of pressurized faults can be ultimately stable or unstable depending on whether the initial shear stress state is greater or lower than the fault residual strength. In the former case the shear crack propagates with a moderate velocity (quasi-static) as it is induced by fluid pressure diffusion (but it might turns into a dynamic instability followed by an arrest). In the latter case, the shear crack initially propagates quasi-statically; then, as slip accumulate along the fault, the quasi-static crack growth become unstable and the shear crack runs away. The effect of dilatancy leads to a local reduction of pore-pressure at the shear crack tip. Notably, the local pore pressure drop and the consequent local increment of effective stress depends on the hydraulic diffusivity of the fault: we expect higher pressure drop for fault characterized by constant permeability (no change with fault dilatancy) than for fault whose permeability increase with dilatant hardening. So it is clear that there is an interplay be- tween pressure drop associated with dilatant hardening and fault permeability change. In this contribution we want to investigate such an interplay for both ultimately stable and unstable faults.