Equilibrium domain wall thickness and number of domains in rectangular magnetic grains are determined by using a modified Amar model. It is shown that domain structure, particularly domain wall thickness, in a magnetized grain depends strongly on grain shape and orientation. These dependencies are attributed to the existence of two competing self-magnetostatic interactions, one from the ends of the grain and the other from the sides. One of the consequences of this is that the thermal variation of domain wall thickness in an elongated grain is greater (smaller) than predicted by classical theory when the grain is magnetized along the shortest (longest) dimension. For magnetite, classical theory provides a good approximation in predicting both domain wall thickness and number of domains in equal-dimensional grains larger than about 4 μm.