In this paper, experiments were conducted on jointed rock mass to study characteristics of elastic wave propagation under different loading conditions. Firstly, by comparing the amplitude and velocity of the elastic wave with the damage degree of rock mass, the macroscopic damage variable of jointed rock mass were characterized by the amplitude of elastic wave. Then, the mesoscopic damage variable was defined through the statistical strength theory. Afterwards, on the basis of the continuous damage theory, a constitutive model by coupling macroscopic and mesoscopic joints was established. Finally, the model was verified and analyzed by combining experimental data. The study shows that, for the intact rock, initiation and propagation of mesoscopic cracks have less effect on the amplitude and velocity of elastic wave. However, for jointed rock mass, the opening and closing of macroscopic joints have a great effect on them. The amplitude and velocity of elastic wave have similar variation law when jointed rock mass is subjected to external force. In comparison with the elastic wave velocity, the attenuation of elastic wave amplitude is sensitive to the changes of the damage degree of jointed rock mass. Thus, it can be used to characterize the macroscopic damage variable of rock mass. Under different loading methods, the damage characteristic of jointed rock mass is determined by macroscopic and mesoscopic joints and its stress state. Therefore, the constitutive model can well reflect damage mechanical properties of jointed rock mass under different stress paths. In triaxial compression tests, the effect of macroscopic joints on the damage of rock mass in the direction of axial compressive stress plays a significant role in the middle and later period of the experiment. While in triaxial tension and compression tests, the macroscopic joint maintains its effect on the damage of rock mass in the direction of axial tensile stress within the whole process of the experiment.