The problem of finding effective characteristics of the nanostructure consisting of spherical shells (nanomatryoshka) is solved using the matrix homogenization method. According to the problem formulation, each of the system layers possesses piezoelectric and/or piezomagnetic properties. Thus, the mutual influence of the elastic, electrical, and magnetic characteristics of the shells on their homogenized values is investigated. In particular, the dependence of the dielectric and magnetic permittivity on the geometrical parameters of the layers is studied and analyzed. The performance of the model is illustrated for a two-layer structure.