The response of a solid subjected to intense blast pressures depends on the ratio of the applied pressures to the stresses (yield stress, etc.) characteristic of the material of the solid. When this ratio is small, the solid can be expected to respond elastically. The paper develops the elastic theory of a semi-infinite solid exposed to a blast initiated at a point on the surface, assumed to be in air at sea level. The results are explicit expressions for the displacements and stresses for early time, small radial distances, and shallow depths. Application to the case where the solid represents the earth is discussed.