The electronic structure and bonding properties of the rare earth metal boron carbide materials containing boron-carbon zigzag chains are analyzed and compared by means of extended Huckel tight-binding calculations. The results show that an ionic picture between the metallic framework, and the boron-carbon chains can easily explain the arrangement, regular or distorted, of the latter. Thus, a formal charge of 3- per BC unit accounts for the regular chains encountered in YBC and UBC. With a formal charge greater than 3- per BC unit, distorted chains due to a peierls instability are expected as in UB0.78C1.22, ThBC, and Th3B2C3. In the three-dimensional materials, the metal-non-metal bonding occurs primarily through electron donation from the anionic sublattice toward the metallic elements. Metallic behavior is expected for all the materials. The structural arrangement in the different MBC compounds is discussed.