A new approach, using stress functions, reveals how each component of the stress regime affects the stress pattern around the wellbore. The effect of tectonic far field stress on the stress trajectories in the host rock near a wellbore is visualized in a series of plots with the analytical stress trajectory solutions for a large range of net pressures on the wellbore. The deviatoric stresses around a wellbore result from the dynamic superposition of (1) far field tectonic stress, (2) near wellbore stress due to lithostatic pressure near the open hole, (3) pore over-pressure or under-pressure in the host rock, and (4) hydraulic pressure applied on the wellbore. The principal stress trajectory plots are used to determine the suitable options for well orientations and to delineate stress trajectory control of the incipient brittle failure patterns for hydrofracs and wellbore breakouts. Our approach provides fundamental insight, with an important practical application for improved understanding of the growth of hydrofractures.