The electronic states of carriers between two concentric spheres of Kane-type semiconductor are theoretically investigated and compared with the results of the parabolic band approximation. Calculations are performed for a hard-wall confinement potential and the eigenstates and the eigenvalues of the Kane Hamiltonian are obtained. Taking into account the real band structure (strong spin-orbital interaction, narrow band gap), the size dependence of the energy of electrons, light holes, and spin-orbital splitting holes in InSb semiconductor concentric spheres are calculated. According to the obtained results both in parabolic and nonparabolic (Kane model) cases, the electron energy levels come close to each other with the increasing of the radius. Copyright (c) 2006.