Various approximations of construction of pseudo-potentials have been considered.The basic attention is given to two directions of the theory of pseudo-potentials: norm-conserving pseudo-potentials (NCP) and modeling pseudo-potentials of type Heine-Abarenkov (MP of type ХАА), based on electronic properties of free ions. Parameters of NCP receive from "the first principles", that is their calculations are based on known laws of quantum mechanics and world constants. Parameters of MP of type ХАА are calculated from valence electron energy in the field of the free ion, received of known spectroscopic experimental data. The special attention is given to comparison of construction principles of NCP and smooth modeling potential (SMP). It is shown, that these principles are co-ordinated. Affirms, that the SNMP can appear smoother, than the smoothest the NCP. (Smoothness of pseudo-potentials is one of theory requirements). The technique of receiving the SMP parameters for free ions is considered in detail. It is shown, that there is a linear dependence between parameters SNMP of ions of simple metals and energy of valence electron. This linear dependence can allowed us to receive SNMP for simple metals in condensed state. Such SNMP will be possible to use for a prediction physical properties of metals and alloys at change of an electronic environment of ions in the condensed condition of metals and alloys.