Abstract: Driving-in piles are widely used in the constructionengineering. There are many theoretical and practical problems with thecompaction effects of pile driving on the soil. Generally, the process ofpile penetration occurs in the semi-infinite and stratified soil. Singlepile has spatial axial symmetry, and the shape and length of piles aredifferent. Therefore, squeezing model due to pile-driving is developed inthis paper to study the effect of the final shape and displacement boundaryof pile wall, stress-free ground surface, the finite length of pile andnon-linearity of soil material. Displacement, strain and stress solutionsare then obtained based on variation principal and their convergence ofimproper integral is also verified. The theoretical scheme is validatedusing passive soil pressure theory, classical CEM results and the numericalsimulation results with Ansys code. The theoretical results illustrate theconvergent three-dimensional improper integral of energy functional and thevalidity of variational solutions.