Magnetic hysteresis has been simulated in grains of magnetite for the size range 0.1--0.7 μm. This was achieved using an unconstrained three-dimensional micromagnetic model of single grains of magnetite with cubic magnetocrystalline anisotropy. Hysteresis loops were obtained for fields applied along both the easy and hard magnetocrystalline axes. Both discrete (Barkhausen) jumps and gradual changes in the magnetic structure are seen, and the reversal of the magnetization can be followed from near saturation in a normal field to a similar state in a reverse field. Predictions of coercivity agree well with published experimental data for unstressed cubic grains of magnetite. ¿ American Geophysical Union 1995