Laboratory and field results have shown the orientation of a hydraulically propagated fracture is not always perpendicular to that of the minimum principal stress but may be influenced by local weakness planes such as preexisting natural fissures; the lower the flow rate, the stronger the weakness planes influence. This observation has led to a new stress determination method based on the measurement of the normal stress supported by fracture planes, with various dips and strikes. This new method provides means to evaluate the precision of the stress determination and can be applied to situations in which none of the principal stresses is vertical. When all the fracture planes are parallel to the borehole axis, the method is still applicable if fast flow rate reopening pressures can be measured and if the principal stress directions are assumed to be independent of depth. Validity of the method is illustrated by analyzing results from two sets of data, one of which has been discussed previously in the literature.