The design of feedback control laws for discrete models of flexible structures is addressed. Two strategies are proposed. First, a parameter optimization method is used, in which the behavior of the controller is described by a performance measure and numerically optimized. A second method, based on continuation maps, allows several performance criterion to be met. These performance measures are quite general in nature; they may be functions of eigenvalues, eigenvectors, sensitivities, and other mission specific quantities. A model of a cantilevered flexible beam is developed and used to demonstrate capabilities and problems with the design methods. / M.S.