The current technology manifests a great demand for high precision and high positioning accuracy in many engineering applications that range from robot manipulators and high-speed flexible mechanisms to supercritical rotors and the space deployable structures. Active control is an important technique for suppressing vibrations in flexible mechanical systems where passive controllers may become either ineffective or impractical. A finite element model of the system dynamics in conjunction with modal reduction methods is introduced. The developed model accounts for the structural material damping. Pointwise observation and control are implemented using two sets of sensors and actuators, respectively. The developed computational active modal control algorithm is applied to the reduced order model of a double span elastic beam, and the dynamic responses of both the controlled and the residual frequency subsystems are numerically evaluated.