A determination problem of external, surface-distributed controlling load that transfers a circular elastic plate from one prescribed initial state as close as possible to another prescribed finite state in a fixed period of time is considered. The problem is posed as a minimization problem of terminal quadratic quality functional on solutions to a linear equation that describes plate vibrations with controls in the right-hand side of the equation. Controls depend only on time, and their distribution on the plate surface is fixed. To solve this control problem, a dual regularized method is applied. A description of the solution algorithm is given, estimates of a rate of functional convergence and conditions of control convergence are obtained.