Abstract: A methcmatical model of grain size affacting the fluidity of liquid alloys is derived based on the mechanism of chock-off at the tip of advancing stream owing to independent crystallisation. Connected the model with H, two fomulas of alloy composition, freezing range, fluidity are got out. The parameter H is used for evaluating the ability of grain refinement of alloying elements, and shows the relation between the composition at the phase diagram corner, C₀<k₀ C_E, and grain size.