Numerical analysis procedures for bifurcation behaviors of symmetric systems with dihedral group symmetry are presented. The branch switching at simple bifurcation points presented in Chap. 2 is extended to double bifurcation points of these systems. In the bifurcation analysis of the systems, rules of bifurcation in Chap. 9 are utilized. As useful numerical procedures for such systems, a revised scaled-corrector method and a block-diagonalization method are advanced. Chapters 7, 8, 9, and 13 lay foundations of this chapter.