A previously published two-dimensional discrete particle simulation model for radial mixing behavior of various slowly rotating drums for solid-state fermentation (SSF) has been extended to a three-dimensional model that also predicts axial mixing. Radial and axial mixing characteristics were predicted for three different drum designs: (1) without baffles; (2) with straight baffles; and (3) with curved baffles. The axial mixing behavior was studied experimentally with video- and image-analysis techniques. In the drum without baffles and with curved baffles the predicted mixing behavior matched the observed behavior adequately. The predicted axial mixing behavior in the drum with straight baffles was predicted less accurately, and it appeared to be strongly dependent on particle rotation, which was in contrast to the other drum designs. In the drum with curved baffles complete mixing in the radial and axial direction was achieved much faster than in the other designs; that is, it was already achieved after three to four rotations. This drum design may therefore be very well suited to SSF. It is concluded that discrete particle simulations provide valuable detailed knowledge about particle transport processes, and this may help to understand and optimize related heat and mass transfer processes in SSF.