Relation between the snap-back (Class II behavior in rock mechanics) of axial stress-axial strain curve of rock specimen in uniaxial compression subjected to shear failure in the form of a single shear band and the snap-back of axial stress-lateral strain curve was investigated analytically. In strain-softening stage beyond the peak compressive stress

the axial and lateral elastic strains were determined by Hooke’s law

while the axial and lateral plastic strains were derived by gradient-dependent plasticity where an characteristic length controls the thickness of shear band. The axial and lateral plastic strains are concerned with the compressive stress level

the inclination angle and the thickness of shear band

the softening modulus

and the geometrical size of rock specimen. According to the signs of the post-peak slopes of axial stress-axial strain curve and axial stress-lateral strain curve

the conditions of axial and lateral snap-backs were proposed. The reason for axial snap-back is that the recovery of axial elastic strain is faster than the increase of axial plastic strain. Similarly

the reason for lateral snap-back is that the recovery of lateral elastic strain is faster than the increase of lateral plastic strain. If the tangent of the inclination angle of shear band is less than Poisson’s ratio multiplied by the ratio of width to height of the specimen

then the snap-back in axial direction occurs once the lateral snap-back takes place. Otherwise

the lateral snap-back occurs when the axial snap-back takes place. For the commonly used rock specimen (height/width is about 2) in laboratory

the lateral snap-back leads to the axial snap-back. In the strain-softening stage

the axial strain-lateral strain curve can be classified into four categories: axial snap-back and lateral snap-back

axial snap-through (Class I behavior) and lateral snap-through

axial snap-back and lateral snap-through

and axial snap-through and lateral snap-back. Conditions of these four kinds of cases were presented.