Abstract:Snap-back instability of rock specimen and testing machine–specimen system are investigated. The direct shear testing machine is simplified as a steel block with certain length and elastic shear modulus. Based on gradient-dependent plasticity,the localized shear band is initiated at peak shear stress and a closed-form analytical solution on shear stress-shear strain curve in strain-softening stage is proposed. If the length of block is zero,the simplified solution can be applied to rock specimen subjected to direct shear. If snap-back of the system occurs, the structural response of the specimen is uncertain (namely,both snap-back and snap-through are possible). When the ratio of length-to-shear elastic modulus increases,the system can lose its stability easily. For the larger ratio, though snap-back of the specimen does not occur,the system will be unstable certainly. But,for the lower ratio, only if the specimen exhibits snap-back,snap-back of the system is possible. Besides,the snap-back of a specimen must lead to snap-back instability of the system. If snap-back is impossible for the specimen,both snap-back instability and snap-through are possible for the system. Some experimental results on rock failure are explained based on the presented theoretical analysis,though the experimental results seem difficult in understanding.