Abstract: There are many analysis methods to determine the ultimate bearing capacity of single pile by using the load-settlement curve obtained from the static load test, but so far, reasonable and theoretical calculation method to solve the ultimate bearing capacity of single pile has not been found. Therefore, the cusp catastrophe model was used to attempt to analyze the load-settlement curve obtained from the static load test so as to evaluate the ultimate bearing capacity of single pile. Through using Matlab software to directly fit the load-settlement curve obtained from the static load test with the evaluation standard of the sudden change characteristic value, the ultimate bearing capacity of the single pile was determined. The results show that: (1) comparing and analyzing the widely used methods for solving the cusp mutation model with the direct fitting method proposed in the present study, the widely used solution methods have shortcomings such as instability and misjudgment, and the evaluation results do not match the actual situation of static load tests. (2) The potential function obtained by direct fitting method is characterized by uniqueness, primacy, and monotonicity, whose calculation results are consistent with the actual situation of the static load test of the single pile. The dirrect fitting method solved the problems of instability and misjudgment existing in the general solution method. Compared to the current pile detection code, the calculation results from direct fitting method are safer. The direct fitting method presented in this study provides a theoretical basis for determining the ultimate bearing capacity of larger diameter piles under slow deformation conditions using 0.05D of pile top settlement as the standard.