The analytical formulas for determining optimum parameters of Maxwell model-defined fluid dampers used to link two adjacent structures are derived in this paper using the principle of minimizing the averaged vibration energy of either the primary structure or the two adjacent structures under a white-noise ground excitation. Each structure is modelled as a single-degree-of-freedom system, which is connected to the other structure through a Maxwell model-defined fluid damper. The derived formulas explicitly express the optimum parameters of the fluid damper, ies the relaxation time and the damping coefficient at zero frequency, as the functions of the frequency and mass ratios of two adjacent structures. The dynamic analysis shows that the fluid damper of optimum parameters can significantly reduce the dynamic responses of most adjacent structures under the white-noise ground excitation. The fluid damper of optimum parameters is then applied to the adjacent structures subjected to either a filtered white-noise ground excitation or the El Centro 1940 NS ground excitation. The results demonstrate that the fluid damper of optimum parameters derived based on the white-noise ground excitation is also beneficial to reduce the responses of the adjacent structures under the filtered white-noise ground excitation and the El Centro ground excitation.