We investigate the effect of hotspot reheating on the intraplate stress field by modeling the three-dimensional thermal stress field produced by nonuniform temperature changes in an elastic plate. Temperature perturbations are calculated assuming that the lithosphere is heated by a source in the lower part of the thermal lithosphere. A thermal stress model for the elastic lithosphere is calculated by superposing the stress fields resulting from temperature changes in small individual elements. The stress in an elastic plate resulting from a temperature change in each small element is expressed as an infinite series, wherein each term is a source or an image modified from a closed-form half-space solution. We apply the thermal stress solution to midplate swells in oceanic lithosphere with various thermal structures and plate velocities. Our results predict a stress field with a maximum deviatoric stress on the order of 100 MPa (1 kbar) covering a broad area around the hotspot plume. The predicted principal stress orientations show a complicated geographical pattern, with horizontal extension perpendicular to the hotspot track at shallow depths and compression along the track near the bottom of the elastic lithosphere. Although stress data near oceanic swells are limited, the source parameters of intraplate earthquakes near several hotspots are consistent with the thermal stress model. These results indicate that thermal stress due to reheating may be an important contributor to stress fields near hotspots in old oceanic lithosphere. ¿American Geophysical Union 1991