Blasting operations are one of the most important parts of geotechnical and mining projects. Most rocks naturally have a series of discontinuities that significantly affect their responses to blast waves. In this paper, the propagation of a blast wave in one intact rock and four rocks with different joint conditions are simulated by a 3-dimensional distinct element code. The results showed that the joint in the model acted as a wave barrier and passed part of the waves, absorbed a portion, and reflected the remaining part into the model. In other words, a discontinuity reduces the energy of the wave and causes more wave attenuation. In addition, a shorter distance between the joint and the hole causes slower wave propagation and greater damping. Moreover, the results showed that the smaller the angle between the discontinuity and axis of the blast holes, the more stress occurs in the rock bench.