The aim of this work is to solve problems of active damping of vibrations in some given domain of a continuous viscoelastic structure. A mathematical model of the mechanical system, the sources of perturbing vibrations, the control system, and the different absorption criteria to be compared are defined. The problems are set in infinite dimension spaces, and the approximate problems are derived in finite dimension spaces. Two methods of resolution are proposed and the solutions are compared. Numerical results simulating the response of a square plate submitted to flexural vibrations are presented for three different absorption criteria, thus permitting a quick evaluation of the comparative effectiveness of the chosen criteria.