The main criterion of the soil cultivation quality is tilling depth. The goal is to predict the trajectory of penetration and steady tool movement as well as the trajectory when hitting an obstacle and leaving it after the obstacle was hit. Factors that actively influence the trajectory can be the tractor motion speed, geometry and weightimplement and tiller tool. For this purpose on the basis of the number of hypotheses differential equation of front and rear mounted implements vibrations is composed relative to the tractor location in a vertical plane along the axis of its movement. In the hypothesis of the force interaction of toolswith soil main provisions proposed by Professor L.V. Gyachev are developed. Mechanical models of the mounted implement are built on the basis of simplifications. In particular, the position of tool at different movement moments is determined by some predetermined function of the generalized coordinate. For the generalized coordinate a rotational angle of the lower hitch links is selected. The pointed out dependence is named as the transmission function of the hitch. By setting in the differential equations of motion various external influences and by changing the power parameters of working bodies, it is possible to imitate changes of soil medium. Such mathematical models allow to simulate movement not only within real operation conditions but that is often more important, to simulate the tools operation in conditions that in practice cannot be created. This is achieved, for example, when we set very hard and long or set very light and short tools, very hard or very soft soil, etc. So you can more clearly see the new phenomena and trends that are difficult to suppose and impossible to see in the real conditions.As a result, new solutions to traditional problems appear.