The nucleon scattering on even–even nuclei in the medium-energy region has been analyzed on the basis of microscopic optical potential (OP) obtained from nuclear-matter calculations with using effective density-dependent nucleon–nucleon interaction of Skyrme type with taking account of the rearrangement potential. Calculations have been performed for volume integrals and rms radii of nucleon–nucleus OP, for energy dependencies of total and total reaction cross sections of neutron– and proton–nucleus scattering and for differential cross sections of the elastic neutron scattering at several energies on various target nuclei. Comparison of the calculation results for the mentioned quantities with corresponding experimental data has been carried out, which has shown a principal possibility of their reasonable description in the framework of the model under consideration.