A new structure-vibration-control approach is proposed which uses a passive coupling element between two parallel structures to reduce the seismic response of a system due to earthquake excitation. Dynamic characteristics of the two coupled single-degree-freedom systems subject to stationary white-noise excitation are examined by means of statistical energy analysis (SEA) techniques. Optimal parameters of the passive coupling element such as damping and stiffness under different circumstances are determined with an emphasis on the influence of the structural parameters of the system on the optimal parameters and control effectiveness. Numerical results including the root mean square values of the response due to the filtered white-noise excitation and the time-histories of response to El Centro 1940 NS excitation are presented.