In this paper, the quantitative research of sand and soal vibrating liquefaction potential is made with 2-dimentional information distribution concept and the formula of fuzzy approximate inferrence. Based on the data of sand and soil vibrating Iiquefaction potential collected by Japanese scholars, Kohji Tokimasu and Yoshiaki Yoshimi, at one hundred places all over the world, fuzzy relation (R)hasbeen established among stress ratio (τd/σ₀¹), normalized standard penetration test (N₁) and sand and soil vibrating liquefaction potential. The deta the author collected on 45 historical liquefaction spots are verified with this method and the results show that the rate of success accounts for 82 per cent of the total.