Materials atomic structure, ground-state and physical properties as well as their chemical reactivity mainly are determined by electronic structure. When first-principles methods of studying the electronic structure acquire good predictive power, the best approach would be to design new functional materials theoretically and then check experimentally only most perspective ones. In the paper, the semi-classical model of multi-electron atom is constructed, which makes it possible to calculate analytically (in special functions) the electronic structure of atomic particles themselves and materials as their associated systems. Expected relative accuracy makes a few percent, what is quite acceptable for materials science purposes.