<p>Piezoceramics are the most widely used class of piezoelectric materials. In a homogeneous macro-volume, they are uniformly polarized along the polarization axis and are transversely isotropic. Foam-like piezoceramic metamaterials have complex geometry, can consist of multidirectional blocks, and, therefore, can be nonuniformly polarized. Studying the effective properties of such materials requires qualitatively new approaches to solving homogenization problems. Here, symmetric Gibson-Ashby cells and regular lattices composed of these cells were considered as an example of such metamaterials. Effective moduli were determined by numerically solving boundary value problems of homogenization using the finite element method, considering the inhomogeneous properties of piezoceramic materials of cells and lattices. The influence of four polarization models and geometric characteristics of cells on the effective moduli was analyzed. The results showed the importance of taking into account the inhomogeneous polarization and demonstrated the possibility of obtaining unusual effective properties that are absent in conventional piezoceramics. Thus, the effective transverse piezomoduli can reverse signs compared to the signs of the corresponding piezomoduli of dense piezoceramics. For other piezomoduli, the dependencies on the volume fraction of voids and on the sizes of the internal cell frames change significantly.</p>