Relativistic density-functional calculations on free Hg2, Hg4, Hg8, Pb2 and Pb4 clusters, and those clusters embedded in an alkali (A) atom surrounding are reported. Heavy metal-metal (M-M) distances, binding energies and effective charges have been calculated. The Hg-Hg distance in the weakly bound free clusters is over 330 pm. Upon embedding in an alkali surrounding, the bonding is strengthened; the bond lengths are reduced for square planar Hg4 to below 300 pm. The bonding in the hypothetical tetrahedral alkali-mercury cluster appear to be quite different, where Hg4 will under a transition to four Hg1. This explains the strict preference of square over the tetrahedral geometry of Hg4 clusters in amalgams. Pb4 is predicted to be stable in a pure cluster and does not show significantly different bonding feature in the lead-alkali crystal. The effective charges on Hg and Pb are calculated to be -0.4 and -0.6, respectively. The bonding characteristics are also examined by calculation of the M4-An interaction energies. The amalgamation energies lie in the range of 50 to 70 kJ/molHg. The formation energy of alkali-Pb is up to 150 kJ/molPb, much stronger than that of alkali-Hg.