The calculation and analysis of single pile settlement was one of the important geotechnical engineering issues, and many geotechnical engineers and scholars investigated and formed a systematic analysis method. Among the existing methods of analysis methods, the elasticity theory method was relatively mature. However, the traditional elasticity theory method could not consider the slip properties between pile and soil, and did not match the actual working properties of pile foundation. In this paper, based on Mindlin's solution, the pile is assumed to be elastic and the relationship between shear stress and relative displacement at the pile-soil interface is assumed to follow hyperbolic function, then series equations were derived and solved by Finite Difference Method. Two cases were demonstrated and the computed results agreed very well with testing data. The advantage of the analysis method proposed was that the interaction of pile and pile, and pile and soil can be considered.