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We discuss the relationship between symmetry and stability in both fluids and structures. Concerning the former, we show that in fluid-structure interactions, symmetry appears essential for stability, since lift forces appear only if non-symmetric solutions exist. We also present a situation in which the solutions of an evolution Navier–Stokes problem converge to the steady symmetric solution for large times. As for the sole structure, instead, we show that a symmetric isolated two-span beam may be more prone to develop instability than an asymmetric one. Thus, symmetry may be disadvantageous from a purely structural point of view.