Abstract：irstly，the dissipated energies induced by axial and lateral plastic deformations of rock specimens under uniaxial compression and the relation between them are analysed. Based on gradient-dependent plasticity in which the thickness of shear band is determined by characteristic length of rock，analytical solutions of dissipated energies in axial and lateral directions of rock specimens in uniaxial compression are derived，respectively. The presented theoretical results show that dissipated energy consumed by shear band is composed of two parts，axial and lateral dissipated energies. Dissipated energy due to axial plastic deformation is proportional to that of lateral plastic deformation and the proportional coefficient is dependent on inclination angle of shear band. According to the actual measured value of shear band inclination，the dissipated energy of axial plastic deformation is greater than that of lateral plastic deformation. As flow compressive stress approaches zero，the dissipated energy by shear band，the dissipated energies of axial and lateral plastic deformations attain their maxima. Bigger inclination angle of shear band leads to bigger dissipated energy of lateral plastic deformation and smaller dissipated energy of lateral plastic deformation. Secondly，shear instabilities of axial and lateral deformations of rock specimens in uniaxial compression are investigated. Shear stress between shear band and elastic rock outside the band is decomposed to horizontal and vertical shear stresses. Similarly，plastic shear deformation of shear band is divided into axial and lateral deformations. Relation between the horizontal shear stress and lateral plastic deformation and relation between the vertical shear stress and axial plastic deformation are presented，respectively. It is shown that the slope of horizontal shear stress-lateral plastic deformation curve is equal to that of vertical shear stress-axial plastic deformation curve. The two curves are dependent on the structural size，therefore，the slope cannot be taken as a constitutive parameter of rock materials. Based on theory of stiffness，instability criterions of specimens composed of shear band and elastic rock outside the band in the axial and lateral directions are proposed analytically. The two criterions are identical，which depend on constitutive relation of rock materials and structural size of rock specimens.
