A numerical-analytical solution to the “effective modulus problem” of transversally isotropic porous ceramics is obtained, taking into account its initial stressed state and the ellipsoidal shape of oriented pores of various connectivity based on the solution of the associated stochastic boundary value problem of electroelasticity of composite mechanics using the Green’s function method. A numerical calculation of the initial and resulting values of the effective piezoelectric modulus of porous piezoceramics (PZT-4) was carried out depending on the values of the volume fraction, shape parameter and connectivity of ellipsoidal, in particular: spherical, disk or tunnel pores, taking into account the initial stressed state of the porous piezoceramics due to its initial axisymmetric deformation. Characteristic values of the volume fraction of spherical and disk pores are identified, taking into account their connections, at which the sign of the numerical values of the initial effective piezoelectric modulus changes with respect to the corresponding module of PZT-4 monolithic ceramics. The values of the volume fraction, shape parameter and type of pore connectivity at which the maximum gradients of the linear dependence of the values of the resulting piezoelectric modulus of porous piezoceramics on its initial macrodeformations are realized are determined. An analysis of graphs of continuous dependences of the initial and resulting values of the effective piezoelectric modulus on the pore shape parameter is given for various cases of their volumetric content, connectivity and axisymmetric initial deformations of porous piezoceramics.