The stability of metal cluster systems relatively to the change of the shape of positive charged core from the volume structure to hollow clusters is considered. Calculations have been done within the jellium model for the core and the Hartree-Fock approach and the Density Functional Theory for the electronic system. For systems with the spherical symmetry two stable states with the different core positive charge distributions have been found: the ordinary metal cluster with volume distribution and the new fullerene-like state with the distribution as the spherical layer with the definite width.