Systematic first principles calculations have been carried out to study the electronic structure and elastic properties of ternary scandium based antiperovskite carbides and nitrides. The calculated ground state properties agree well with the experimental and other theoretical results. The elastic constants are predicted from which all the related mechanical properties are calculated. From the analysis of the ratio of bulk modulus to shear modulus, we conclude that the above mentioned antiperovskites are brittle in nature with a considerable elastic anisotropy. The band structure shows a pronounced hybridization of Sc-d states with the p states of C or N at the Fermi level. It is observed that the changes brought about in the mechanical properties of Sc-based cubic inverse perovskites when replacing C by N are less pronounced than that for the Ti based antiperovskite carbides and nitrides, where it is quite noticeable. A possible reason for the change in behavior is also analyzed. © 2011 Elsevier Ltd. All rights reserved.