In many hot spot--ridge systems, formation of off-axis volcanic chains or lineaments occurs between the hot spot centers and nearby mid-ocean ridges. In some cases, such as Gal¿pagos, Kerguelen, and possibly the Mid-Pac Mountains and Tristan, these lineaments appear to meet in a focus zone near the hot spot and fan outward in the direction of the ridge axis. The origins of these lineaments are not well known and do not easily fit into typical conceptual models of ridge or hot spot volcanism. It has been proposed for the Gal¿pagos region that such lineaments are caused by channeling of hot asthenosphere from off-axis mantle plumes toward mid-ocean ridges, where enhanced volcanism initiates island formation (Morgan, 1978). Alternatively, other workers suggest that these lineaments are controlled by patterns of stress in the lithosphere. We examine this latter hypothesis by considering the effects of buoyant uplift and asthenospheric shear on the base of the lithosphere induced by an expanding mantle plume. Using thin plate theory, we calculate the two-dimensional (plan view) pattern of depth-integrated stresses in a plate of varying thickness. Both a straight, continuous ridge and a ridge-transform-ridge system are simulated by a displacement discontinuity, boundary element model. Ridge and transform segments have imposed normal and zero shear tractions, and we test different idealized tectonic or far-field stress conditions. Assuming that volcanism is promoted by lithospheric tension and aligns along lineaments parallel to trajectories of least tensile stress, calculations reproduce the rough fan-shaped pattern of lineaments between the Gal¿pagos Archipelago and the Gal¿pagos Spreading Center. The focus of the fan shape is over the plume center when it interacts with a straight ridge, but the fan focus appears closer to a segmented ridge, offset by a transform fault, if the ridge segments are more tensile than the far-field stress. This condition provides a plausible explanation for the apparent focus at the Gal¿pagos north of the hot spot center. The width of the fan pattern along the ridge axis is predicted to increase as the plume-ridge separation increases and as the far-field stress becomes more tensile parallel to the ridge. The observed width along the Gal¿pagos Spreading Center is consistent with a nearly isotropic remote stress. Models predict the lithospheric tension caused by plumes to promote lineament formation on only young lithosphere. In support of this prediction, a compilation of data from 23 hot spots shows that lineament formation is common near hot spots with plume-ridge separations of <1250 km or on lithosphere of <25 Ma, but not on older lithosphere.