Abstract: Deep penetration in displacement piles involves large deformation, nonlinear contact and other mechanical difficult issues. They are key technical problems in numerical modelling. An arbitrary Lagrangian–Eulerian method is used to overcome these problems. The penetration is simulated by the given continual displacement boundary at the top of jacked piles. The grid remesh algorithm and data transmission are studied. The penetration of premoulded piles in sand is analysed, and it is proposed that the arbitrary Lagrangian–Eulerian method is an effctive way to solve large deformation in penetration problem.