The chemical bonding and elastic properties of $Ti_2AC$ (A = Ga, Tl) have been investigated by means of extended H$ddot{u}$ckel tight-binding band structure calculations. The bulk modulus of $Ti_2AC$ decreases as Ga is replaced with Tl at the A sites. This can be understood by considering the relative strength of Ti-A bonds resulting from the different atomic size of 3A-group elements. The analysis of the projected density of states (PDOS) and the crystal orbital overlap population (COOP) for the respective phases shows that Ti-Ga bonds in $Ti_2GaC$ are stronger than Ti-Tl bonds in $Ti_2TlC$.