Ab initio calculation of the Elastic and Optical properties of cubic half-Heusler compounds MCoSb (M = Ti, Zr and Hf) are reported using the FP-LAPW approach of the Density Functional Theory. Generalized Gradient Approximation was used as the exchange and correlation potential for investigating these properties. It was found that the Bulk modulus decreases with the increase in temperature and increases with the increase in pressure for all of the three Heusler compounds under study. The Debye's temperature along with compressional, Shear and average elastic wave velocities has also been calculated. The elastic results are compared with the available theoretical and experimental works. The optical investigation of the compounds shows high reflectivity at the infrared region of the photon energy. The imaginary part of the dielectric function reveled the optically non-metallic behavior of the MCoSb compounds, with optical band gap being around 1 eV.

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