Nuclear analytical methods during the last decades have given a lot of new data on elemental composition of various natural materials. These data allow a return to the question of the regularities of elements abundance. This question seems to be important from the point of view of basic science as well as analytical chemistry (analytical procedure planning, expected element concentrations, choice of sufficient sensitivity and reproducibility, etc.). The most fruitful approach in this connection is the comparison of the elemental composition of some generalized systems with an element's fundamental characteristics and/or its position in the Periodical System. Stronger correlations can be found when the elemental characteristic (its position in the Periodic Table) versus abundance is considered within separate groups of elements. This idea is illustrated by considering elements' abundance in the Universe, Solar System, Earth crust, sea water, soils, plants, etc. Simple equations describe these functions with acceptable agreement of tabular and calculated data. The coefficients of these equations in many cases were also connected with some fundamental characteristics such as ionization potential, ion potential, melting and boiling point, etc.