Stress redistribution induced by excavation results in the tensile zone in parts of the surrounding rock mass. It is significant to analyze the localization of deformation and damage, and to study the complete stress-strain relation for mesoscopic heterogeneous rock under dynamic uniaxial tensile loading. On the basis of micromechanics, the complete stress-strain relation including linear elasticity, nonlinear hardening, rapid stress drop and strain softening is obtained. The behaviors of rapid stress drop and strain softening are due to localization of deformation and damage. The constitutive model, which analyze localization of deformation and damage, is distinct from the conventional model. Theoretical predictions have shown to consistent with the experimental results.