In this study, a structural modeling and an analysis considering structural stability were investigated to develop an icosahedron-based hemispherical modular dome. To design the dome, a program that can perform icosahedron shape modeling, modularization of joint connection members. Furthermore, based on the adopted numerical model, the buckling mode, unstable behavior characteristics according to load vector, and the critical buckling load of the modular dome under uniformly distributed load and concentrated load were analyzed, and the resistance capacities according to different load vectors were compared.