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In the current paradigm of cold dark matter cosmology, large-scale structures are assembling through hierarchical clustering of matter. In this process, an important role is played by megaparsec (Mpc)–scale cosmic shock waves, arising in gravity-driven supersonic flows of intergalactic matter onto dark matter–dominated collapsing structures such as pancakes, filaments, and clusters of galaxies. Here, we report Very Large Array telescope observations of giant (∼2 Mpc by 1.6 Mpc), ring-shaped nonthermal radio-emitting structures, found at the outskirts of the rich cluster of galaxies Abell 3376. These structures may trace the elusive shock waves of cosmological large-scale matter flows, which are energetic enough to power them. These radio sources may also be the acceleration sites where magnetic shocks are possibly boosting cosmic-ray particles with energies of up to 1018 to 1019 electron volts.