Abstract: According to multi-support stochastic earthquake ground motion model, a three-dimensional earthquake and multi-support stochastic earthquake ground motion model was established. Then based on the pseudo excitation method (PEM), a random vibration methodology was formulated for the seismic analysis of multi-supported structures subjected to spatially varying ground motions. The ground motion spatial variability consisted of traveling-wave effect, incoherence effect and local site effect. The seismic response of a super long latticed roof was analyzed in detail. It shows that all these effects have significant influence on the seismic response of the structure. On the other hand, it shows the pseudo excitation method is efficient and precise and is applicable to the random seismic response analysis of the long-span structure under multi-dimensional and multi-support excitation.