This paper presents optimization of the response of coupled structures subjected to random excitation. The dynamic system involves discrete and continuous models of coupled structures. The structures are assumed to be subjected to white noise excitation of known power spectral density. The mean square response of the structure is taken as the objective function. The physical properties such as length, thickness, stiffness and damping are taken as the design variables. The discrete system is assumed to be subjected to two kinds of excitation; band-limited white noise excitation and ideal white noise excitation. Coupling stiffness and damping characteristics are used as design variables. For the case of continuous coupled beam model, band-limited white noise excitation is considered and the root mean square response of the structure is minimized for a range of excitation frequency. Geometric properties of the structure are used as design variables.