In this chapter, we employ ab initio approaches to review some important physical properties of nanolaminated ternary carbides MAX phases. We fi rstly use an all electron full-potential linearized augmented plane-wave method within the generalized gradient approximation and the density functional theory approaches, to explore the existence of a steric effect on the M site in these compounds. The elastic properties are also reported in order to assess the mechanical stability. The substitution of oxygen for carbon in Ti 2 SnC M n +1 AX n, forming Ti 2 SnC 1- x O x, is examined next, where we simulated the effect of oxygen incorporation on mechanical and electronic properties using projector augmented wave method. We show that oxygen has interesting effects on both of elastic and electronic properties, that the bulk modulus decreases when oxygen concentration increases. The bonding in Ti 2 SnC 1- x O x has a tendency to a covalent-ionic nature with the presence of metallic character. © 2012 Woodhead Publishing Limited.