Half metallic ferromagnetism is reported in RbTiO<sub>3</sub> and CsTiO<sub>3</sub> compounds under the exchange correlation functions GGA, TB-mBJ and GGA+U using full potential linearized augmented plane wave method. Spin resolved calculations are carried out and implemented within the framework of density functional theory. The compounds exhibit energy band gap in spin up direction using three functional of PBE-GGA, TB-mBJ and GGA+U. A larger band gap is predicted to occur in both the compounds with the use of TB-mBJ potential. A higher value of magnetic moment is evidenced for RbTiO<sub>3</sub> and CsTiO<sub>3</sub> using PBE-GGA method as compared to mBJ and GGA+U methods. Curie temperature has been determined for the compounds at equilibrium and reduced volumes. It is reported that Curie temperature increases with the increase of hydrostatic pressure. With the help of second order elastic constants, Debye temperature and anisotropy factor have been predicted for the compounds.