Surface tensions of low carbon slabs and 16 mass%Cr stainless steel were estimated using a surface thermodynamic model proposed by Mukai et al. As an application of the model, an index to evaluate the driving force for the fine bubble entrapment by the solidifying shell, the Mukai-value, M, was calculated from the surface tension values. The relationship between Mukai-value and number of entrapped bubbles was discussed. A linear relationship was found between the number of captured bubbles and Mukaivalue. In the previous work, the Mukai-value was used as a relative scale to evaluate the driving force for the movement of bubbles. However, by calculating the M from the surface tension values by the surface thermodynamic model, physically reasonable Mukai-values could be obtained.