The sodium expansion curves of semi-graphitic cathode and TiB2/C composite cathode with different TiB2 contents were measured with the improved Rapoport-Samoilenko apparatus. The mathematic model of the sodium expansion was deduced on the basis of the experimental results. The sodium expansion parameter (a) and penetration rate factor (Q), were introduced into the model. The model was validated with the experimental sodium expansion curves self-measured and reported. The results show that the variation tendency of the sodium expansion parameter (a) and penetration rate factor (Q) is consistent with that of the experimental curves. The model is capable of not only conveniently judging the cathode quality, but also favorably establishing a unified standard of the resistance to sodium penetration of cathode. The sodium expansion curves of semi-graphitic cathode and TiB2 / C composite cathode with different TiB2 contents were measured with the improved Rapoport-Samoilenko apparatus. The mathematic model of the sodium expansion was deduced on the basis of the experimental results. The sodium expansion parameter The model was validated with the experimental sodium expansion curves self-measured and reported. The results show that the variation tendency of the sodium expansion parameter (a) and penetration rate factor (Q) is consistent with that of the experimental curves. The model is capable of not only conveniently judging the cathode quality, but also favorably establishing a unified standard of the resistance to sodium penetration of cathode.