A series solution is presented for a hemispheroidal elastic inhomogeneity at the free surface of an elastic half space. The loading is either all around tension at infinity, perpendicular to the axis of symmetry of the inhomogeneity, or uniform, nonshear type eigenstrains sustained by the inhomogeneity. The displacement potentials of Boussinesq are used to represent the solution and several numerical calculations are performed to illustrate the results.

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