In determining the safety of foundations the assumption is usually made that the pressure distribution on the ground, in general unknown, is closely approximated by a constant one. Mathematically, the problem is thereby reduced to finding the components of stress and displacement in a half-space due to a uniform pressure on a portion of its plane boundary. The present paper contains an investigation of this problem for the case of loading over an area bounded by an ellipse. Two of the results are: (a) On the normal to the loading area through its center, the two principal stresses in planes parallel to the undeformed surface, compressive on and near the surface, become tensile within a depth smaller than the length of the corresponding principal axis of the loading area; (b) the normal deflection of the surface is greater at the extremity of the minor axis of the loading area than at the extremity of the major axis, the difference between the two values increasing with the ellipticity of the bounding curve.