It is discussed the problem of an optimal control for the circular plate's linear vibrations, when the distributive disposed forces influence on it. The problem is solved by the method of variable division and it is brought to the differential game, which is described by the infinitesimal differential equations of second order. The extremal strategies are constructed by the extreme targeting method. It is shown that if the resources of the first player are more than the resources of the second player and the influencing forces belong to class L₂, then the problem of damping of plate's vibrations is solved.