When a space frame that is symmetrical with respect to two orthogonal planes is subjected to cyclic horizontal loading, there exist critical states peculiar to the conditions under cyclic loading in the inelastic range. The states have been defined as the symmetry limit and the in-plane limit. At those limits, transitions are possible from symmetrical behaviors to asymmetrical behaviors with respect to either of the two symmetrical planes. Those limits cannot be predicted by any classical bifurcation theory and new theories for finding those limits have been formed as the symmetry-limit theory and in-plane-limit theory, respectively. In this paper, a finite element analysis method is proposed for finding the symmetry limit and the in-plane limit of space frames subjected to cyclic horizontal displacement. Analyses are performed for two types of one-story space frames based on the proposed method. As a result of the analyses, displacement amplitudes and bifurcation modes of the in-plane limit and the symmetry limit are obtained, respectively. Accuracy of those limits is verified by hysteretic response analyses for the frames.