In this paper are shown dynamic models which represent the real systems. As an example, one gear couple has been presented. In this case, the simplified model two discrete masses with elastic and damped connections. Using the of mechanics and taking into account initial and basic principles conditions, the system of differential equations is established which describes physicality of motion. Such system of equations represents mathematical model at dynamical behavior of gear transmission. Established system of differential equations has been solved in analytical way with the aim of obtaining data for numerical analysis. The proper estimate of dynamical behavior of gear transmission and other systems can be on the basis of own frequency and of own form of oscillating. In the paper is presented the solution of the main form of oscillating and stress condition using finite elements method.