We examine the neutrality of an elliptical inhomogeneity embedded in a particular class of compressible hyperelastic materials of harmonic type when a uniform Piola stress field is prescribed in the surrounding matrix. The present method is based on a spring-type imperfect interface model and on the proper choice of imperfect interface function, which realizes the same degree of imperfection in both normal and tangential directions. The analysis indicates that, in general, the neutral shape and the single imperfect interface function are both dependent on the magnitude of the prescribed stress field.