Abstract <p>This work investigates the mechanical properties of B2-type CoTi material, using the density functional theory within the pseudopotential method and a plane waves basis set as implemented in the Quantum Espresso code. Our calculation yielded values of Debye temperature θ_D = 414.6 K and elastic constants <i>C</i>₁₁&#xa0;=&#xa0;226.50 GPa, <i>C</i>₁₂ = 129.55 GPa, and <i>C</i>₄₄ = 226.50 GPa, respectively. To test the incertitude of calculated elastic constants <i>C</i>_<i>ij</i> for B2-type CoTi intermetallic compound, we compared our obtained results with the experimental values of the literature. Our findings show a good agreement with experimental data. Furthermore, using an approximation based on the quasi-harmonic model, we explore various thermodynamic properties of the B2-type CoTi intermetallic compound. The thermodynamic properties obtained in this study reveal that the free energy decreases gradually with the augmentation of the temperature, while both the heat capacity as well as the entropy increase with the raising of the temperature. At <i>T</i> = 298 K, our calculation yielded values of entropy <i>S</i> = 68.35 J mol^–1 K^–1 and heat capacity <i>C</i>_V = 46.61 J mol^–1 K^–1, respectively. To the authors’ knowledge, no previous study has reported theoretical data on the thermodynamic properties for CoTi material.</p>