A modification of the model Fues potential based on taking into account the effects of Coulomb screening and polarization of the core in the ground and lower excited states of many-electron atoms in the parameters of this potential is proposed. Numerical values of parameters of the modified model potential are obtained for the ground states of alkali metal, alkaline earth, and inert gas atoms and for the metastable triplet state of helium. The numerical values of polarizabilities and hyperpolarizabilities calculated with the use of the modified potential are in significantly better agreement (as compared to the results obtained by using the traditional approach) with the most accurate literature data.