Abstract. In this paper we consider the formulation and solution of the task of a dynamic synthesis machine with an asynchronous electric motor and a slider-crank mechanism. The constant parameters of the slider-crank mechanism (mass and moments of inertia and centers of gravity of links) and the parameters of the electrical motor are defined. The laws of motion of the machine and kinematic parameters of the mechanism are considered as given. We have developed the method of optimal dynamic synthesis of the machine, which consists of an asynchronous electric motor and a slider-crank mechanism. The criterion of optimization of the dynamic synthesis of a machine is the root mean square sum of the moments of driving forces, the forces of resistance and inertia forces which are reduced to the axis of rotation of the crank. The method of optimal dynamic synthesis of a machine can be used in the design of new and the improvement of known mechanisms and machines.