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Inhomogeneous displacement profiles have been derived for a single‐rod composite and a single‐tube 1‐3 ceramic‐polymer composite under both uniaxial and hydrostatic stress. The effective piezoelectric constants for the composites have been derived in terms of the ceramic content, the piezoelectric and elastic constants of each component, and the aspect ratio of the ceramic rod. The stress concentration inside both phases is derived from the calculated inhomogeneous displacement profiles. It is found that only a finite portion of the polymer in the vicinity of the ceramic‐polymer interface actually contributes to the stress transfer, and the induced additional stress on the ceramic also has a higher magnitude near the interface. The theoretical results quantitatively predict the performance of a given 1‐3 structure, and can be used to optimize the design parameters, such as ceramic content, aspect ratio of the ceramic rods, rod geometry and rod arrangement, resin hardness, etc., for 1‐3 structures designed for specific purposes.