The present paper aims at studying the seismic response of structures equipped with viscoelastic dampers (VED). The performance of such a passive control system is here analyzed using the energy balance concept, which leads to an optimal design process. The methodology is based on an energy index (EDI) whose maximization permits determination of the optimal mechanical characteristics of VED. On the basis of a single degree of freedom model, it is shown that the maximum value of EDI corresponds to a simultaneous optimization of the significant kinematic and static response quantities, independently of the input. By using the proposed procedure, the optimal design of new and existing structures equipped with VED, inserted in traditional bracing systems, are here analyzed and discussed.