We used Density Functional Theory (DFT) calculations to investigate the structural, electronic, magnetic, mechanical and thermodynamic properties of CoYSb (Y = Cr, Mo and W) compounds. These are XYZ type half-Heusler alloys, which also exist in the face centred cubic MgAgAs-type structure and conform to F¯43m space group. We computed these properties in three different atomic arrangements known as Type-I, Type-II and Type-III phases. In all these phases, the alloys were found to be in the ferromagnetic state. Furthermore, the calculated electronic band structure and the total electronic density of states indicated a metallic behaviour in CoWSb, nearly half-metallic in CoMoSb and half-metallic in CoCrSb, with a minority-spin band gap of 0.81 eV. Furthermore, the calculated mechanical properties predicted an anisotropic behaviour of these alloys in their stable phase. Finally, due to its high Debye temperature value, CoCrSb shows stronger covalent bonding than CoMoSb and CoWSb, respectively.