Ti2AlB0.5C0.5 and Ti2AlN0.5C0.5 compounds which are called M2AX type MAX phases referred to as 211 and have hexagonal crystal structure with conform to P63/mmc space group, have been examined by using Generalized Gradient Approximation (GGA) in the Density Functional Theory (DFT) as implemented in CASTEP software package. In this study, the electronic, elastic, and lattice dynamical properties of these compounds have been investigatedwithin the ab initio study. These compounds show metallic behavior since there is no band gap in the calculated electronic band structures. The estimated elastic constants of these compounds indicate that they are mechanically stable and their bonding nature is ionic and also, Ti2AlN0.5C0.5 compund has anisotropic character in mechanically whereas the behavior of Ti2AlB0.5C0.5 compound is nearly isotropic. Moreover, both of our compounds are brittle materials. Also, these compounds are dynamically stable since there are no soft modes in their plotted phonon dispersion curves.