A formulation is developed for modal response analysis of multi-support structures using a random vibration approach. The spectral moments of the structural response are rigorously decomposed into contributions from spectral moments of uncoupled modal responses. An advantage of the proposed formulation is that the total dynamic response can be obtained on the basis of mode by mode uncoupled analyses. The contributions to the total response from modal responses under individual support ground motions and under cross-correlated pairs of support ground motions can be recognized explicitly. The application and performance of the formulation is illustrated by means of an example using a well-established coherency spectrum model and widely known power spectra models, such as white noise and Kanai-Tajimi. The first three spectral moments of displacement, shear, and bending moment responses are computed, showing that the formulation produces the same results as the exact solution.