Pressure induced structural phase transitions in SnAs and SnSb have been studied using ab-initio density functional theory. The phase transition from NaCl to CsCl structure occurs at 29.8GPa for SnAs, which agrees well with experimental data, while the same for SnSb is found to be 10.6GPa, reported for the first time. The calculated ground state properties are in good agreement with available experimental and theoretical results. The electronic and bonding properties have also been analyzed. The elastic constants along with other secondary elasticity properties in B1 (NaCl-type) phase are also estimated at ambient as well as high pressure.