MP2 calculations of the stacking energy are reported for the dimers of a set of polycyclic aromatic hydrocarbons. The interaction strengths and their dependence on the shape-dependent measures as well as the aromatic character of the monomer are studied. For small systems involving four to six rings, the noncovalent interactions seem to be independent of the shape of the monomers. The most preferred conformations for parallel stacked dimers are not aligned exactly but off-center with small shifts; however, these shifts are on the order of 1 angstrom, and the energy necessary to keep them aligned is less than 0.5 kcal/mol per ring. Small-angle rotations within the molecular planes also do not require much energy, and in some cases they lead to stronger interactions.