A structure M≤ N is symmetrically embedded in N if any σ∈ Aut (M) extends to an automorphism of N. A countable structure M is symmetrically indivisible if for any coloring of M by two colors there exists a monochromatic M≤ M such that M∼= M and M is symmetrically embedded in M. We give a model-theoretic proof of the symmetric indivisibility of Rado's countable random graph [9] and use these new techniques to prove that Q and the generic countable triangle-free graph Γ△ are symmetrically indivisible. Symmetric