This work is devoted to the elucidation of the applicability of the jellium model to the descriptionof alkali cluster properties. We compare the jellium model results with those derived within ab initio theoretical approaches and with experiments. On the basis of Hartree�Fock and local-density approximations we have calculated the binding energies per atom, ionization potentials, deformation parameters and optimized values of the Wigner�Seitz radii for neutral and singly charged sodium clusters with the number of atoms N≤20. The characteristics calculated within the framework of the deformed jellium model are compared with the results derived from ab initio simulations of cluster electronic and ionic structure based on density functional theory and systematic post Hartree�Fock many-body perturbation theory accounting for all electrons in the system. The comparison performed demonstrates the great role of the cluster shape deformations in the formation cluster properties and quite reasonable level of applicability of the deformed jellium model. This elucidates the similarities of atomic cluster physics with the physics of atomic nuclei.