Coherent short-wavelength radiation from laser–plasma interactions is of increasing interest in disciplines including ultrafast biomolecular imaging and attosecond physics. Using solid targets instead of atomic gases could enable the generation of coherent extreme ultraviolet radiation with higher energy and more energetic photons. Here we present the generation of extreme ultraviolet radiation through coherent high-harmonic generation from self-induced oscillatory flying mirrors—a new-generation mechanism established in a long underdense plasma on a solid target. Using a 30-fs, 100-TW Ti:sapphire laser, we obtain wavelengths as short as 4.9 nm for an optimized level of amplified spontaneous emission. Particle-in-cell simulations show that oscillatory flying electron nanosheets form in a long underdense plasma, and suggest that the high-harmonic generation is caused by reflection of the laser pulse from electron nanosheets. We expect this extreme ultraviolet radiation to be valuable in realizing a compact X-ray instrument for research in biomolecular imaging and attosecond physics.