The elastic and thermal properties of ScRu under pressure are studied using a first-principles pseudopotential method within the generalized gradient approximation. The calculated lattice parameter and formation enthalpy are in good agreement with the previous experimental and theoretical results. From the static finite strain technique, we obtained three independent elastic constants (C 11 , C 12 and C 44 ) and various secondary elasticity parameters such as shear modulus, Young's modulus and elastic anisotropy, as functions of pressure. This study also provided the pressure and temperature variations of the bulk modulus, Debye temperature, thermal expansion coefficient and heat capacity in wide pressure (0-60 GPa) and temperature (0-1800 K) ranges.