Abstract: Although much work has been done on seismic analysis for large span space lattice structures subjected to multi-dimensional multi-support excitations, its extreme value distribution of the stochastic response remains unaddressed. Analytical solutions can be obtained only in simple cases involving strong assumptions using the traditional level-crossing process theory; the diffusion process theory is just feasible for SDOF system. Based on this, the recently developed probability density evolution method is used to capture extreme value of large span space lattice structures subjected to multi-dimensional multi-support excitations. A virtual stochastic process is firstly constructed, then PDEM is built to evaluate extreme value distribution, and dynamic reliability of space structures can be obtained through simple integration. To verify the efficiency and accuracy of the introduced approach, the reliability and extreme value distribution of a long span single layer lattice shell structure under multi-dimensional multi-support excitations are observed. The results agree well with the ones obtained by the stochastic simulation method, so the introduced PDEM is of accuracy, efficiency and versatility.