Dynamic response of two adjacent single degree-of-freedom (SDOF) structures connected with friction damper under base excitation is investigated. The base excitation is modeled as a stationary white-noise random process. As the force-deformation behavior of friction damper is non linear, the dynamic response of connected structures is obtained using the equivalent linearization technique. It is observed that there exists an optimum value of the limiting frictional force of the damper for which the mean square displacement and the mean square absolute acceleration responses of the connected structures attains the minimum value. The close form expressions for the optimum value of damper frictional force and corresponding mean square responses of the coupled undamped structures are derived. These expressions can be used for initial optimal design of the friction damper for connected structures. A parametric study is also carried out to investigate the influence of system parameters such as frequency ratio and mass ratio on the response of the coupled structures. It has been observed that the frequency ratio has significant effect on the performance of the friction damper, whereas the effects of mass ratio are marginal. Finally, the verification of the derived close from expressions is made by correlating the response of connected structures under real earthquake excitations.