As is widely accepted, the crucial event of the progress of Alzheimer's disease is the formation of extracellular neurotoxic amyloid plaques, consisting mainly of 40 or 42 amino acid residues, in the brain. Zinc and copper metal ions are involved in this process, since they enhance the amyloid beta aggregation and are incorporated into plaques. In this paper we have analyzed theoretically the energetics implied in the formation of some complexes of both cations, adopting a number of models that take into account various coordination environments. The aim was to determine which among the coordination patterns examined is the favoured one in order to give better insight in the controversy concerning the metal binding site of amyloid beta peptide.