In this work, the magnetothermal characteristics and magnetocaloric effect in YFe3 and HoFe3 compounds are calculated as function of temperature and magnetic field. These properties were investigated using the two-sublattice mean field model and the first-principles DFT calculation using the WIEN2k code. The two-sublattice model of the mean-field theory was used to calculate the temperature and field-dependences of magnetization, magnetic heat capacity, magnetic entropy, and the isothermal change in entropy ∆Sm. We used the WIEN2k code to determine the elastic constants and, subsequently, the bulk and shear moduli, the Debye temperature, and the density-of-states at Ef. According to the Hill prediction, YFe3 has bulk and shear moduli of roughly 99.3 and 101.2 GPa respectively. The Debye temperature is ≈ 500 K, and the average sound speed is ≈ 4167 m/s. In fields up to 60 kOe and at temperatures up to and above the Curie point for both substances, the trapezoidal method was used to determine ∆Sm. For instance, the highest ∆Sm values for YFe3 and HoFe3 in 30 kOe are approximately 0.8 and 0.12 J/mol. K, respectively. For the Y and Ho systems, respectively, the adiabatic temperature change in a 3 T field decreases at a rate of around 1.3 and 0.4 K/T. The ferro (or ferrimagnetic) to paramagnetic phase change in these two compounds, as indicated by the temperature and field dependences of the magnetothermal and magnetocaloric properties, ∆Sm and ∆Tad, is a second-order phase transition. The Arrott plots and the universal curve for YFe3 were also calculated and their features give an additional support to the second order nature of the phase transition.