Lattice　shell　is　a　type　of　spatial　structure　whose　vibrations　are　dominated　by　both　horizontal　and　vertical　motion.　In　this　paper,　a　multi-dimensional　pseudo　excitation　method　is　developed　for　nonstationary　random　seismic　analysis　of　structures　under　multi-support　and　multi-dimensional　earthquake　excitations,　in　which　the　phase　lags　between　the　excitations　have　been　involved.　Mathematical　formulations　are　derived.　A　method　of　evaluating　peak　responses　is　recommended.　Multi-dimensional　seismic　random　models　are　discussed.　A　random　vibration　analysis　is　performed　for　a　double-layer　cylindrical　lattice　shell　to　investigate　its　seismic　performance.　It　is　shown　that　the　developed　method　is　a　highly　efficient　algorithm,　which　can　easily　solve　the　nonstationary　problem　of　large　structures　under　multi-support　and　multi-dimensional　earthquake　excitations.