We investigate the cohesive energy, heat of formation, elastic constant and electronic band structure of transition metal diborides TMB₂ (TM =  Hf, Ta, W, Re, Os and Ir, Pt) in the Pmmn space group using the ab initio pseudopotential total energy method. Our calculations indicate that there is a relationship between elastic constant and valence electron concentration (VEC): the bulk modulus and shear modulus achieve their maximum when the VEC is in the range of 6.8–7.2. In addition, trends in the elastic constant are well explained in terms of electronic band structure analysis, e.g., occupation of valence electrons in states near the Fermi level, which determines the cohesive energy and elastic properties. The maximum in bulk modulus and shear modulus is attributed to the nearly complete filling of TM d–B p bonding states without filling the antibonding states. On the basis of the observed relationship, we predict that alloying W and Re in the orthorhombic structure OsB₂ might be harder than alloying the Ir element. Indeed, the further calculations confirmed this expectation.