The failure property of inhomogenous brittle materials under plate impact experiment has been studied by using AOW (amphibolized olivine websterite) rock as a representative sample. A small recompression signal was observed in the VISAR record of the rear free surface velocity at shock stress much below σHEL, indicating the generation of the failure wave. By using samples with different thickness but impacted at approximately the same shock stress of 3.9 GPa, the trajectory of the propagation of the failure wave through the stressed sample has been determined. The failure wave is generated with a delay time of about 0.5 μs behind the shock wave front, and propagates into the stressed material with a velocity comparable to that of the shock wave front. A physical mechanism involving the “in situ activation and growth” of the originally existing micro-cracks due to the local shear stress under shock wave compression is suggested for these observations.