The results of a computer simulation of the structure of periodic grain boundaries between twin related crystals of aluminium are described. An interatomic potential derived on the basis of pseudo-potential theory was used. The algorithm employed allows simultaneous local atomic relaxation and rigid body translation of the adjacent grains. It was found that rigid body translation is a dominant contribution to relaxation, and that the energy of a boundary, $\gamma $, is not simply related to boundary periodicity. In addition, annealing twins in aluminium were observed by using transmission electron microscopy and detailed correspondence with theoretical predictions was found in two areas; the calculated $\gamma $'s of experimentally observed boundary planes were lower than those of geometrically possible alternatives, and excellent agreement between predicted and experimentally measured rigid body translations was obtained for two types of tilt boundary.