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The theory of oscillation processes is the field of the science associated with mathematics, mechanics and general physics. I.Newton, L.Eiler, LaGrange and other classics of mechanics laid the basement of a modern theory of mechanical oscillations. Khristian Huigens, the wellknown Holland scientist and the watchmaker (16291695) contributed greatly into the theory of oscillation. He created izochronic cycloidal pendulum and was the first to observe selfsynchronization of associated oscillating systems. J.Y.Strett (Lord Raley, 18421919) a British scientist created a systematic teaching on oscillation forms about their attenuation in the XIX century. he investigated a problem on plates' and sheaths' vibration in details. At the same time A.Poincarre (18541912) for the first time proposed an idea of a qualitative analysis of oscillating systems using depiction of motion at a phase plane and related this depiction to the facts of periodical and nonperiodical motions, stability and so on. He merited also a mathematical analysis of complex linear oscillations which he conceived in the form of a great number of ordinary linear oscillations. The soviet scientists L.I.Mandelshtam (18791944), N.D.Papaleksi (18801947), A.A.Andropov (19011952), N.M.Krylov (18791955), N.N.Bogolyubov, Yu. A.Mitroopolsky, A.N.Krylov, V.V.Bolotin, I.I.Blechman, Yu. I.Neimark, Ya. G.Panovko, G.F.Ganiyev and others contributed greatly in creation of modern methods of theoretical analysis of oscillating systems. Two directions may be singled out in the present science on oscillations: 1. Development of theory, schematization of real objects, creation ofidealized models using the laws of mechanics and mathematical apparatus; 2. Application of instruments for measurement of the values characterizing actual motion of one or another object. Experimental grounding of the theory by vibrodiagnostical methods. The author carried out his investigations by these two directions. He passed from the development of the linear theory of stability that has been covered in the previous books to elaboration of the linear theory of oscillations built on an idea of analogy in a form of free oscillations of constructions. Varying a load, specifying the concepts of dynamical stability and instability taking into account the load's effect by introducing the coefficient of the load, the author offers new scientific results which agree well with the experiment. Prof. Alexander Petrovich Leschenko was born in 1939. He has got PhD degree in Civil Engineering. Prof. Leschenko has 3 Certificates on his discoveries in the field of Structural Mechanics: 1) Certificate DO N 000008 on discovery Principle of pairing of force factors; 2) Certificate DO N 000006 on discovery Phenomena of separating torsional strains of elastic bars; 3) Certificate DO N 000007 on discovery Specific analogy law in stability and oscillation of an elastic system; and 2 patents on his inventions: 1) Patent N 2150098 of 27.05.2000 on invention Testing method for buckling failure of metal constructions; 2) Patent N 542435 of 21.09.1978 on invention Breakdown controller of pile driver. His current research concerns various aspects of Civil Engeneering and Structural Mechanics. The publication list comprises the following books:  Structural mechanics of thinwalled structures (in Russian), Moscow, Stroyizdat, 1989;  New principles in structural mechanics of thinwalled structures (in Russian), Moscow, Stroyizdat, 1995;  Fundamental structural mechanics of elastic systems (in Russian), Taganrog, Sphinx, 2003. 