Theoretical anhysteretic magnetization curves are derived by searching for the minimum energy in an applied field of model domain structures. Magnetization curves are derived for: (1) Finite uniaxial crystals with 180$^\circ$ plane parallel walls. (2) Slightly misoriented polycrystals with (a) plane parallel walls, (b) walls allowed to bow. (3) Oriented polycrystalline materials with air gaps at the grain boundaries. The third model is found to be unrealistic, for a polycrystalline material without any second phase at the grain boundaries, and it is shown that the observed magnetization behaviour may be more generally accounted for in terms of the misorientation between grains. The calculations are precise, but the results are dependent on the initial choice of model domain structure and any limitations imposed on the way in which the walls move.