The structure-property relations of ternary copper chalcogenides, $TlCu_{3-x}S_2$ and $alpha-BaCu_{2-x}S_2$ are examined. The density of states, band dispersions, and Fermi surfaces of these compounds are investigated to verify the reason of the metal-insulator transitions by extended Huckel tight-binding band calculations. The origin of the metalinsulator transitions of non-stoichiometric $TlCu_{3-x}S_2$ and $alpha-BaCu_{2-x}S_2$ is thought to be the electronic instability induced by their Fermi surface nesting.