We have predicted the phase transition pressure (PT)and high pressure behavior of Zirconium and Niobium carbide (ZrC, NbC). The high pressure structural phase transitions in ZrC and NbC has been studied by using a two body inter-ionic potential model, which includes the Coulomb screening effect, due to the semi-metallic nature of these compounds. These transition metal carbides have been found to undergo NaCl (B1) to CsCl (B2)-type structural phase transition, at high pressure like other binary systems. We predict such structural transformation in ZrC and NbC at a pressure of 98GPa and 85GPa respectively. We have also predicted second order elastic constant and bulk modulus. The present theoretical work has been compared with the corresponding experimental data and prediction of LAPW and GGA and LDA theories.