Abstract: This paper presents a geometrical nonlinear finite element analysis for bellows under arbitrary load. Considering the structural characteristics, the bellows was idealized as a series of conical frusta elements with two nodes, joined at nodal circles. The load and displacement were expanded in Fourier series in circumferential angle. The geometrical nonlinear equations of bellows were derived in the Updated Lagrangian formulation and discreted by finite element method. The geometrical nonlinear analysis of bellows can be completed effectively by using incremental load method and NewtonRaphson iterative method. The numerical results show that the method is rational.