We study the transversally isotropic piezo-ceramics PZT-4 with ellipsoidal pours oriented in the direction of the axis of symmetry. Using the singular approximation of the method of periodic components, we obtain characteristics of effective elastic penetrability, piezo-mechanical penetrability, dielectric penetrability, and basic coefficients of electric-mechanical links. We study how the geometry of ellipsoidal pours and their inclusion volume fraction influence on the effective characteristics mentioned above and on the values of the stress invariants of the skeleton of porous piezo-ceramics.