The seismic response spectrum analysis of structures is time-consuming under multi-support excitations. The seismic spectral response of structures can be expressed based on several correlation coefficients and the time consumption can be greatly reduced if the coefficients are expressed in closed-form. In this paper, approximate expressions of spatial coherence functions are suggested. Then integrals for the coefficients are carried out analytically and their closed-form expressions are obtained. The closed-form expressions are developed from Clough-Penzien’s auto-power spectral density and Hu’s APSD. The numerical results show that the approximate closed-form expressions of correlation coefficients are of enough engineering accuracy and high efficiency for response spectrum method under multi-support excitations.