The proposed criterion for dynamically optimizing the elastic system (ropes) of load-lifting mechanisms of cranes translational motion, which minimizes the dynamic coefficient. The laws of motion of the elements of the lifting mechanism of the crane, in which the specified criterion can be realized, is established. The implemented approach to the dynamic optimization of the elastic system (ropes) of load-lifting mechanisms of cranes their translational motion can be further used in the design of mechatronic control systems by these mechanisms, which can provide for tracking all instantaneous (sudden) changes in the kinematical, as well as power-supply parameters of the specified mechanical systems for various ways of lifting the cargo, namely: weight, with picking up. It takes into account all the overloads of the system that arise in it at the initial stage of lifting the load (at the moment of launch - when lifting the weight; at the moment of separation from the ground (ground) - when raising with lifting). It should be noted that the results obtained in the work can also be used in the design of the actuators of load-lifting mechanisms of cranes operating in those or other regimes, which provide a smooth start of the mechanism, and therefore significantly reduce the dynamic factor both at the time of start and in the period of the main movement, which ends a smooth, not a jump-like final stage of lifting to a complete stop. The results obtained in the work can also be used to refine and improve existing engineering methods for calculating the elastic elements (ropes) of crane lifting mechanisms in order to avoid inevitably arising diverse oscillations in the ropes themselves (longitudinal, bent, twist and combined), as at the stages of their design, construction, as well as in the real-world operation of cable systems of cranes.