In this paper, optimal distribution of a viscoelastic damping layer is sought for suppression of the transient vibration of a flexible beam. For the damping design, eigenvalues in the range of interest are taken as design criteria rather than the responses at a specific frequency. Two eigensensitivity based optimizing procedures are proposed, which are analogous to the pole placement technique and optimal control theory for dynamic system design. For the eigenanalysis of the structure with frequency-dependent material, Golla-Hughes-McTavish (GHM) model is used in expressing the viscoelastic material property and an approximate eigensolution is employed to avoid the intensity of iterative computation in the optimization process which is caused by additional degrees of freedom due to GHM modelling. Optimized partial coverage configurations are illustrated and compared to the full coverage configuration demonstrating the improved vibration characteristic of the optimally layered structure.