To study ellipsoidal and spherical particle flow, clogging behavior and unclogging dynamics, a series of numerical simulations were carried out using our validated 3-D coupled computational fluid dynamics–discrete element method (CFD–DEM) model. For the first time, the strength of clogging arches is assessed in terms of fluid pressure gradient, which can effectively break up the clog. The main findings are as follows. In a clogged assembly, only when the flushing fluid reaches the unclogging pressure gradient, the ellipsoidal and spherical particles can flow in a continuous state. For the ellipsoids and spheres with the same equivalent volume, the unclogging pressure gradient of an ellipsoidal assembly is 11.8 times higher than that of a spherical assembly. Clogging arches at the outlet show the highest strength when the longitudinal orientations of the ellipsoids are perpendicular to the outlet plane. In contrast, the formed arch has the lowest stability when the longitudinal orientations of the ellipsoids are in the same direction as the long side of the outlet, as shown in the graphical abstract. The unclogging pressure gradient of the former case is 1.9 times greater than that of the latter case. The granular arches observed in our 3-D model are categorized as complex 3-D backbone arches. In the flowing region, particles rotate nearly perpendicular to the outlet plane, especially those approaching the outlet. Moreover, triangular stagnant zones are formed on both sides of the bottom of the rectangular box. The model presented here offers a great promise for future investigation of various granular systems at the particle scale.