The analytical method of wave and oscillation theory differential equations periodic solution building on the so-called saw-tooth argument transformation base has been used in the paper series [V.N. Pilipchuk, in: International Congress of Mathematicians, Zurich, 3-11 August 1994, Short Communications, 1994, p. 202; V.N. Pilipchuk, G.A. Starusenko, Izvestiya Nastionaljnoj Akademii Nauk Ukrainy 11 (1997) 25 (in Russian)]. This approach has been developed further, where famous transformation has been generalized on non-symmetrical case. In the present paper the non-symmetrical saw-tooth argument transformation method is suggested to apply to the elasticity theory periodic problems.