Abstract: Damping property of vertically mixed structure, which vertically consists of two or more types of materials, is difficult to identify due to the difference in energy dissipation of different parts of the structure. To perform fundamental structure design, especially using commercial software, the damping ratio is essential, and the concept of equivalent uniform damping ratio is commonly accepted. In this paper, based on the Rayleigh damping model, a formula was proposed for calculating the relative steady-state error of vertically mixed structure by means of decoupling approximation. And then, the optimum equivalent damping ratio was obtained under random ground motion. A vertically mixed structure was typically represented by an equivalent two degree-of-freedom (DOF) oscillator. Its dynamic characteristics were determined by those of sub-structures. The distribution of equivalent damping ratio and the displacement error of this 2-DOF oscillator were plotted as the function of structural parameters. Numerical results demonstrate that the procedure proposed in this paper generates more accurate displacement responses under seismic excitations, while in contrast, the use of single material damping ration may usually lead to a under- or over-estimate of the capability of energy dissipation.