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.