Topographic modification of gravity-induced near-surface stresses results in significant departures from a lithostatic state. A perturbation scheme provides approximate analytical solutions for plane strain of an elastic half-space with an irregularly shaped free surface of small characteristic slope &egr;. The leading order effect of the topography is equivalent to that of a distributed normal load on a plane boundary, and the correction at order &egr; is due to a distributed shear traction on a plane boundary. In the near-surface region, these two effects contribute at the same order to departures from the lithostatic stress field. The contribution of the shearing has been neglected in most previous analyses. We present explicit solutions for several particular geometries: a symmetric ridge or valley, an adjacent ridge and valley, a shelf, and a sharp-crested ridge. Notable features include (1) for a sufficiently steep ridge, the horizontal normal stress is compressive at the crest and decreases, possibly becoming tensile, with depth; (2) large horizontal tension is induced in a valley bottom. At greater depth, these effects vanish, and the stresses approach lithostatic. Similar analysis is applied to a half-space under a far-field tectonic compression or tension. The result shows that the leading order effect of topography is equivalent to a distributed shear traction on a plane surface. Regional horizontal compression can be significantly reduced, or even change to tension, in the neighborhood of a topographic high.