A dynamic model for the rotors tilting mechanics studying of a convertible aircraft, taking into account the elastic and damping characteristics of the mounting units of the tilted lift-cruise thrusters is proposed. To solve the problem, it is proposed to consider the convertiplane as a composite structure of separate pats jointed with each other at the nods. The general mathematical model of the motion of a composite structure consists of independent equations of motion of separate parts of composite structure connected by kinematic conditions with each other. In the equation of motion constructed using the d’Alembert-Lagrange principle, the work of generalized forces - reactions of interaction of the separate pats of the composite structure are added. The advantages of this approach are described. The results of the flight simulation of the convertible aircraft with two tilted lift-cruise units as a composite structure are presented to evaluate the control using the proposed model.