Based on the theory of invariants, polynomialconstitutive relations for transversely isotropic piezoelectricporous materials are derived from the polynomial integrity bases for an energy density function depending on a symmetric second-order tensor and two vectors. They are assumed to be smooth functions of their arguments, are expanded about the values their arguments take in the reference configuration and all terms up to the quadratic terms in the gradients of the mechanical displacement, the electric potential, and the gradients of the volume fraction are kept. The second-order constitutive relations so obtained are then specialized to the case of infinitesimal deformations and weak electric fields, and also to the case of infinitesimal deformations and strong electric fields. Copyright 1995 Acoustical Society of America