For understanding acoustic emission (AE) activity and accumulation of micro-damage inside rock under pure tensile state,the AE signals has been monitored on the test of directly tension on two kinds of marble specimens.A tensile constitutive model was proposed with the damage factor calculated by AE energy rate.The tensile strength of marble was discrete obviously and was sensitive to the inside microdefects and grain composition.With increasing of loading,the tensile stress-strain curve obviously showed nonlinear with the tensile tangent modulus decreasing.In repeated loading cycle,the tensile elastic modulus was less than that in the previous loading cycle because of the generation of micro damage during the prior loading.It means the linear weakening occurring in the specimens.The AE activity was corresponding with occurrence of nonlinear deformation.In the initial loading stage which only elastic deformation happened on the specimens,there were few AE events occurred;while when the nonlinear deformation happened with increasing of loading,lots of AE events were generated.The quantity and energy of AE events were proportionally related to the variation of tensile tangent modulus.The Kaiser effect of AE activity could be clearly observed in tensile cycle loading.Based on the theory of damage mechanics,the damage factor was defined by AE energy rate and the tensile damage constitutive model was proposed which only needed two property constants.The theoretical stress-strain curve was well fitted with the curve plotted with tested datum and the two property constants were easily gotten by the laboratory testing.