AbstractFor proper seismic analysis of secondary systems with multiple supports, the prescription of the seismic input in terms of the conventional pseudo‐acceleration floor response spectra is quite inadequate. It is necessary that the relative velocity floor response spectra as well as the cross floor response spectra, characterizing the correlation between the motions of various floors where the secondary system is attached, be also prescribed as the inputs. In addition to these, it is also necessary to define the floor displacements, velocities and their correlations. In this paper, the methods which can use the ground response spectra directly to obtain these inputs are developed. These methods are based on the random vibration analysis of the supporting primary structure, but still do not require the base input in stochastic form; conventional ground response spectra can be directly used. Numerical results demonstrating the application of the approaches are give