X-ray back diffraction from monolithic two silicon crystal plates of 25-150 microm thickness and a 40-150 microm gap using synchrotron radiation of energy resolution DeltaE = 0.36 meV at 14.4388 keV clearly show resonance fringes inside the energy gap and the total-reflection range for the (12 4 0) reflection. This cavity resonance results from the coherent interaction between the x-ray wave fields generated by the two plates with a gap smaller than the x-ray coherence length. This finding opens up new opportunities for high-resolution and phase-contrast x-ray studies, and may lead to new developments in x-ray optics.