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We analyze the surface morphological stability of a coherently strained thin film grown epitaxially on a thick elastic substrate under the simultaneous action of an electric field that drives surface electromigration. A model of driven film surface morphological evolution is developed and a linear stability analysis is carried out of the planar film surface morphology. The analysis reveals that surface electromigration can inhibit surface morphological instabilities due to the lattice mismatch between the film and the substrate. The critical electric-field strength for surface stabilization and the optimal electric-field direction are determined and the effects of surface diffusional anisotropy are examined.