We consider the optimal control of a dynamic process in a plate. As the optimality criterion we take the minimum time for extinguishing an arbitrary type of oscillation. We assume that the expenditures of energy of the control device are limited; for the solution of the problem we take the apparatus of Krein's theory of l-moments. The equation of forced oscillations of a plate has the form DV2V~W ~. 9h~" = q (x, y, t) (1) for the initial conditions (x, v, o) = f (x, v); ~, = g (x, y) (2) and the cor responding bmmdary condit ions. The external load can be taken as a control p a r a m e t e r . Thus, vary ing q(x, y, t), we obtain the opt i mal (from a ce r t a in point of view) cha rac t e r i s t i c s of the dynamic p roces s . Let q(x, y, t) = F ( t ) 5 ( x ~ F ) 6 ( Y V F ) , where 6 is the Dirac delta function; ( F and '~F a re the coordinates of the point of application of F(t). It is n e c e s s a r y to find the control act ion F(t) that, in the min i mttrn possible t ime T, e l iminates the osci l la t ions of the plate, the state of which is desc r ibed by Eq. (1) for known initial and boundary conditions. The total energy of the control device expended in extinguishing the osci l lat ions is bounded by the value 12 i .e. ,