The purpose of this study is to analyze the elasto-plastic response considered geometric nonlinear behaviors for two analysis models with different boundary conditions, and is to investigate dynamic characteristics of single layer reticular domes subjected to vertical and horizontal earthquake motions that are TAFT, KOBE and ELCENTRO. In particular, the aim of numerical analysis is to obtain the maximum acceleration of input earthquake motions to lead the collapse of domes in this dynamic analysis. Analysis models are two kinds of domes with pinned supports and radius direction roller supports. The following results were found through numerical experiments. 1) Generally, when the static safety factor increases, the dome can endure to the greater earthquake motion without collapse in order to increasing the structural capacity. However, a different tendency for the collapse acceleration is seen with Taft and pinned supporting system. Especially, the collapse acceleration declines at from ν_s = 3 to 4.2) In the pinned support system and ν_s = 2, the dynamic collapse starts by a few dimples at side of the dome with the buckled region spreading to its neighborhood. This phenomenon is similar to the mechanism of the domes subjected to the horizontal earthquake motions. On other hand, the dimple of domes with ν_s = 4 causes at the top of it, and the top part of domes thrust out with slowly vibrating or collapse with sinking at top of it. 3) Like the above, the vertical earthquake motion strongly affects not only vibrating states of domes but also dynamic buckling behaviors.