In consideration of the importance of the gas entrainment (GE) phenomena in the design study on sodium-cooled fast reactors. a lot of analytical, experimental and numerical studies have been conducted to investigate the GE behaviors. Such researches are focused mainly on finding out the onset condition of GE and some proposed GE onset models can provide the onset condition conservatively. However, it is still difficult to evaluate the entrained gas flow rate because the gas bubble entrainment at a free surface is accompanied by complicated free surface deformation. In this paper, the authors focus on the GE caused by a free surface vortex and propose a mechanistic model to calculate the entrained gas flow rate. The mechanistic model contains the theoretical equation of transient gas core elongation and the empirical equation of critical gas core length for gas bubble detachment. Based on those two equations, the entrained gas flow rate is calculated as the portion of the gas core elongated beyond the critical gas core length per unit time. Finally, the mechanistic model is applied to the calculation of the entrained gas flow rate in a simple water experiment. As a result, it is confirmed that the entrained gas flow rate grows rapidly when the liquid (water) flow rate, which determine the strength of a free surface vortex, exceeds a certain threshold value.