This paper described the behaviours of four divalent metal fluorides (CaF$_2$, SrF$_2$, CdF$_2$ and BaF$_2$) in terms of their superior elastic, mechanical and thermophysical properties. Initially, higher-order elastic constants of the chosen divalent metal fluorides have been calculated using the Coulomb and Born–Mayer interaction potential in the temperature regime 100–300 K.With the help of these constants, other elastic moduli, such as Young’s modulus (Y ), bulk modulus (B), shear modulus (G), Poisson’s ratio (σ ) and Pugh’s ratio (B/G) have been computed using Voigt–Reuss–Hill approximation. The Born stability criteria and Vicker’s hardness parameter (Hν ) have been used for analysing the nature and strength of the materials. Later on, ultrasonic velocities including Debye average velocities were evaluated using calculated values of second-order elastic constants and density in the samephysical conditions. Thermal properties such as the lattice thermal conductivity, thermal relaxation time, thermalenergy density and acoustic coupling constant have also been computed at the same physical conditions and along $\langle$100$\rangle$. The temperature-dependent ultrasonic properties have been correlated with other thermophysical propertiesto extract important information about the microstructural quality and the nature of the materials. The obtained results have been analysed to explore the inherent properties of the chosen divalent metal fluorides, which are useful for numerous industrial applications.