The reopening behavior of longitudinal cracks which are induced by hydraulic fracturing on the surface of a borehole is analyzed to establish the methodology of hydraulic fracturing tectonic stress measurements. To this end, a model is constructed to analyze the coupled problem of fluid flow in the crack and the crack reopening behavior in impermeable rock, based on the linear theory of elasticity and also on the linear fracture mechanics and taking into account that the crack does not reclose perfectly upon deflation due to crack surface damage and some minor shear displacement. The results show that the borehole pressure at the instant when the crack reopening occurs is just half of the pressure value predicted by the conventional theory. The borehole pressure at which the pressure-time history apparently deviates from a linear behavior is somewhat higher than the true pressure value at the crack reopening, and it increases with water injection rate.