The cumulative response of three granular materials with significantly different grain shape and surface characteristics (glass beads, natural sand with subrounded grains and crushed sand with very angular particles) but identical grain size distribution curve has been studied in drained cyclic triaxial tests. For each material, several tests with 100,000 cycles and different amplitudes, densities, average mean pressures and average stress ratios have been performed. In case of glass beads and natural sand, an approximately square relationship between the residual strain accumulation rates and stress or strain amplitude was found (ε̇acc ∼ εampl2), while an almost proportional dependence was measured for the crushed sand (ε̇acc ∼ εampl). The largest differences in the cumulative response of the three tested materials were observed regarding the pressure-dependence of ε̇acc. For glass beads and (less pronounced) for natural sand, the residual strain accumulation rates decreased with average mean pressure, while the opposite tendency was obtained for the crushed sand. At small pressures, the residual strains were much larger for the glass beads than for the natural sand and particularly the crushed sand, while these differences in the accumulated strains almost diminished at larger pressures. Independent of the shape and the surface characteristics of the particles, it was confirmed that the average stress ratio is the governing parameter of the cyclic flow rule. Finally, the parameters of the high-cycle accumulation (HCA) model proposed by Niemunis et al. (2005) were analyzed considering the grain shape parameters (aspect ratio, circularity) obtained from an automated grain shape analysis.