The azimuth of maximum horizontal stress in a reservoir can vary significantly with depth and with position on a subsurface structure. We present and discuss evidence from field data for such variation and demonstrate both analytically and with finite-element modeling how such changes might take place. Under boundary conditions of uniform far-field displacement, changes in stratigraphic layering can reorient the principal stress direction if the formation is intrinsically anisotropic. If the formation stiffness is lower perpendicular to bedding than parallel to bedding (as is often the case in layered geologic media), an increase in dip will reduce the component of compressive stress in the dip azimuth direction. Folds can reorient principal stresses because flexural strain varies with depth and position. Compressive stress perpendicular to a fold axis increases with depth at the crest of an anticline and decreases with depth at the limb. When the regional stress anisotropy is weak, this change in stress magnitude can reorient the local principal stress directions. Numerical simulations of such effects gave results consistent with changes in stress orientation at the Cymric and Lost Hills oil fields in California as observed via shear-wave polarization analyses and tiltmeter surveys of hydraulic fracturing. Knowledge of such variation of stress direction with depth and structural position is critical for drilling, completions, hydraulic fracture, and well pattern designs.