In this paper issues related to states estimation problem of the drive system with elastic-joint are presented. After a short introduction the mathematical model of the drive is demonstrated. Then the control structure with additional feedbacks is described briefly. Next the classical Luenberger observer is presented. The shortcomings of this system such as sensitivity to improper identification of initial conditions of the states is pointed out. As a solution, the multilayer observer is proposed in order to accelerate the elimination of estimation errors. The proposed methodology is described in detail and the theoretical formulations are supported by experimental tests.