An analytical formulation for seismic analysis of multiply supported secondary systems is developed. The formulation is based on the random vibration theory of structural systems subjected to correlated inputs at several points. The response of the secondary systems is expressed as a combination of the dynamic, pseudo-static and cross response components. The dynamic part is associated with the inertial effect induced by the support accelerations. The pseudo-static part is due to the relative displacement between supports, and the cross part takes into account the correlation between these two parts of the response. The seismic input in this approach is defined in terms of the auto and cross pseudo-acceleration and relative velocity floor spectra. The information about floor displacements and velocities as well as their correlations is required for calculating the pseudo-static and cross response components. These inputs can be directly obtained from the ground response spectra. The interaction effect between the primary and secondary systems is studied. This effect is specially significant when the modes of the secondary system are tuned or nearly tuned to the modes of the primary system. The floor spectral inputs are appropriately modified to take into account this interaction effect. The design response of the secondary system when computed with these modified floor inputs will incorporate the interaction effect. The applicability of the proposed methods is demonstrated by several numerical examples.