In this paper, we investigate the control of 2D flexible structures by vibration confinement and the regulation of their energy flow along prespecified spatial paths. A discretized-model-based feedback strategy, aiming at confining and suppressing simultaneously the vibration, is proposed. It is assumed that the structure consists of parts that are sensitive to vibrations. The control design introduces a new pseudo-modal matrix derived from the computed eigenvectors of the discretized model. Simulations are presented to show the efficacy of the proposed control law. A parametric study is carried out to examine the effects of the different control parameters on the simultaneous confinement and suppression of vibrations. In addition, we conducted a set of simulations to investigate the flow control of vibrational energy during the confinement-suppression process. We found that the energy flow can be regulated via a set of control parameters for different confinement configurations.