The structural, electronic, elastic and thermal properties of two lutatium mono-pnictides (LuAs and LuSb) have been studied using the density functional theory within the generalized gradient approximation. The calculations indicate that there is a structural phase transition from their ambient NaCl – (B 1 ) to CsCl – (B 2 ) structure at 56.7 and 25.2GPa along with the volume collapse percentage of 3% and 5%, respectively. Structural parameters like lattice constant (a 0 ), bulk modulus (B) and pressure derivative of the bulk modulus (B′) are presented. The calculated band structures indicate that B 1 and B 2 phase of these compounds are metallic. We have calculated the second order elastic constants for these compounds. We also compare the ground state (a 0 and B) and high pressure phase transition (P t ) properties for three members of lanthanide series.