The general regular patterns in localization of deformation at pre-failure stage in rocks under compression are found and analyzed (sylvinite, marble sandstone). Applicability of speckle-photography methods to problems on rock deformation and failure is proved. The authors define the self-sustained behavior of the localized plastic deformation in rocks under compression, due to effect of various plastic micromechanisms. The autowaves in rock specimens under compression propagate at a rate of ∼10−5–10−4 m/s (0.3–3 km/yr), which is close to slow motions induced in the earth crust by an earthquake or a rockburst. The ratio of the experimental and calculated failure times is correlated with the coordinates of the failure points in the test rock specimens.