Abstract: Based on the field tests data of five pipe piles, this paper studies mathematically the relationship between pile peak loads and pile peak settlement, as well as the bearing behavior of steel pipe piles in terms of the relationship between pile shaft compression and pile peak loads. Analyzing results are presented in form of curves, and the following conclusions can be drawn. Firstly, Boltzmann model can be use to model the bearing behavior of steel pipe piles, with the correlativity coefficient being over 0.996. Secondly, curves of compositive coefficient versus pile peak loads fall in three types. The compositive coefficients of three short piles are bigger than those of two super-long piles, indicating the compositive coefficient is a variable and can hardly be used to determine the pile shaft compression. Thirdly, Boltzmann model can be used to study the pile shaft compression subjected to pile peak load, with the correlativity coefficient being over 0.996. The compositive correlativity coefficient of 5 piles is 0.9871. Therefore, the pile shaft compression of steel pipe piles can be predicted by existing regression curves and associated equations. Fourthly, Boltzmann mathematic model is appropriate to be used in this study, and it can provide new method for the estimation of pile shaft compression and the determination of ultimate bearing capacity of piles. Finally, ultimate bearing capacity of piles is in negative linear relation with length-diameter ratio.