This paper focuses on the relationships used for estimating the magnitudes of horizontal stresses acting in faulted sedimentary basins. Relationships are derived here based on the assumptions of a faulted but essentially elastic rock and take into account the tectonic stress component associated with active normal and thrust faults, as well as the pore pressure. The equations presented predict that the orientation of the minimum stress can change once a normal or thrust fault has formed. They further predict that an increase in pore pressure gradient will result in a more isotropic stress state. Field data are used to assess the predictions and include stress-depletion measurements from normally faulted basins and stress measurements performed ''at depth'' in compressive tectonic ''thrust'' regions.