The structural, elastic and thermal properties of three heavy monoantimonides of holmium, erbium and thulium (LnSb, Ln=Ho, Er and Tm) have been investigated theoretically by using an interionic potential theory consisting of long-range Coulomb, short-range repulsive and van der Waal’s (vdW) interactions. These compounds exhibit first-order crystallographic phase transition from their initial NaCl-type structure to CsCl-type structure at pressures 27, 33.2 and 29.8GPa for HoSb, ErSb and TmSb, respectively. The values of elastic constants and Debye temperatures as a function of pressure are also reported. The elastic properties such as Young modulus (E), Shear modulus (G), Poisson ratio (υ) and anisotropic ratio (A) in an NaCl-type structure are also predicted.