In order to establish the methodology of hydraulic fracturing tectonic stress measurements, the relation between the so-called reopening pressure of longitudinal cracks and tectonic stresses is studied. To this end, the coupled problem of fluid flow in the crack and the crack reopening behavior in an impermeable rock is analyzed based on the linear theory of elasticity and also on the linear fracture mechanics, where it is taken 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, contrary to the conventional theory, the apparent reopening pressure, i. e., the borehole pressure at which the pressure-time history apparently deviates from a linear behavior, is hardly affected by the maximum horizontal tectonic stress acting in the direction parallel to the crack line. It decreases and approaches the minimum horizontal tectonic stress normal to the crack plane with decreasing injection flow rate. Moreover, it is shown that the results of laboratory hydraulic fracturing experiments conducted in the present work support those conclusions.