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We investigate the use of energetic electron beams for high-resolution radiography of flaws embedded in thick solid objects. A bright, monoenergetic electron beam (with energy >100  MeV) was generated by the process of laser-wakefield acceleration through the interaction of 50-TW, 30-fs laser pulses with a supersonic helium jet. The high energy, low divergence, and small source size of these beams make them ideal for high-resolution radiographic studies of cracks or voids embedded in dense materials that are placed at a large distance from the source. We report radiographic imaging of steel with submillimeter resolution.