In this study, we employed the pseudopotential plane wave approach to examine the influence of the X atom (X = Be, Ca, or Sr) on the physical properties of isostructural chloroperovskites GaXCl3. The GGA-PBEsol and LDA functionals were employed to simulate the exchange-correlation interactions. The computed equilibrium lattice parameters exhibit a high level of concordance with the existing theoretical findings. The cohesion energy and enthalpy of formation were computed to verify the energetic stability of the materials under consideration. The determined values of the single-crystal elastic constants (Cij) indicate that GaBeCl3 remains mechanically stable up to a hydrostatic pressure of 18 GPa. Similarly, GaCaCl3 preserves its stability up to 5 GPa, while GaSrCl3 remains mechanically stable up to 1.25 GPa. The projected Cij values were used to estimate several elastic moduli and related properties, including the shear and bulk moduli, sound wave speeds, Young's modulus, Poisson's ratio, and Debye temperature. The quasiharmonic Debye approach was employed to examine various thermal parameters, including the temperature dependence of the unit cell volume, bulk modulus, expansion coefficient, Debye temperature, isochoric and isobar heat capacities, Grüneisen parameter, and entropy function. It has been shown that GaBeCl3 demonstrates a lower thermal expansion coefficient and a higher Debye temperature in comparison to GaCaCl3 and GaSrCl3.