When cleaning cutting, pruning of branches of roadside trees and shelter belt contour cutters are widely used, cutters is designed for total horizontal, vertical and oblique trimming crowns. These devices are hinged or removable ones and aggregated with wheeled tractors of traction class 0.6 to 1.4 kN, widespread in forestry. Improving the design of such devices is made in the following areas: cutting devices and hydraulic drives. In the proposed working body of the machine for cutting tree crowns containing base machine, crane on the handle of which a rotary hydraulic motor (rotator)is mounted, the shaft of which has movable connection with the housing of the circular saw with one-sided sharpening in the direction of the detachable part of the branch, V-shaped emphasis in the form of unilateral action hydraulic cylinder with spring-loaded rod, piston cavity which is connected in series with the drain lines of the hydraulic motor which is mounted an adjustable throttle to create pressure of the working fluid (support). In this implementation of the device when circular goes deep into the branch, which is cut, the V - shaped support with spring-loaded rod moves all the way in the branch and eliminates the clamping of the saw blade in the cut, which will improve reliability and performance. The article has developed a mathematical model of device for pruning tree crowns by circular saw with hydraulic drive on the basis of common methodology for the simulation of planar mechanisms. Differential equations of the cutting process were composed. The model of proposed design of the device for cutting tree crowns allows to study the influence of geometrical and mechanical parameters of the branches of the trees, technological parameters of cutting process on energy consumption and quality of the cut, taking into account design parameters. The model allows also to assess the performance and to examine the effectiveness of the device in different operating conditions.