Local pressure lows in layered sections perturbed by anticlinal structures are studied analytically using equations for pressure change across interfaces. They are simple equations of pressure difference for low-angle structures and boundary integral equations for steeply dipping anticlines. Pressure may decrease locally near the crests of anticlines, as well as away from them at distances commensurate to the anticline height. Predicting stress patterns, which are specific for different groups of geologic structures, is a difficult task. However, some components of the stress field, such as low-pressure zones which may act as sinks for fluids, are relatively easy to constrain. Stress in these zones depends on the dip of anticlines and their curvature at each surface point. Negative curvature causes additional lateral extension and promotes further decrease of overburden pressure around the crests.