The propagation of finite one-dimensional discontinuities of particulate-phase pressure in dry granular flow is examined. These discontinuities are classified depending on whether the granular pressure behind the discontinuity is larger or smaller than that in front of it. If the speed of propagation of infinitesimal discontinuities is regarded as ’sonic’, the former propagate ’supersonically’, while the latter propagate ’subsonically’. Rarefaction and compression waves are also analyzed, and we show that, based on realistic constitutive assumptions on the density dependence of particulate-phase pressure, rarefaction waves smooth out as they propagate, while compression waves reinforce each other to become shocks.