Since 1993, the LRBB develops, in collaboration with the CIRAD, a tool to calculate the biomachanical behaviour of trees during growth. This tool, called AMAPmeca, which is used in conjunction with the software AMAPpara, allows the relationships between tree architecture and its biomechanical answer to long time loadings to be simulated. The evolution of the shape and the growth stresses are calculated for each cycle of the plant development. The AMAPmeca module relies on the Finite Element Method and uses a linear 3D Bernoulli beam element to discretize the structure. Nevertheless, this theory used small displacements assumption which is not valid when the loads are too high during one cycle of growth. These cases need to use the large deflection theory: it is non-linear structure analysis. We propose to develop a finite beam element in non-linear theory. The Newton-Raphson procedure applied to an Updated Lagrangian Formulation at each iteration is used to solve the equilibrium of structure. The emergence of the geometric (or initial stress) stiffness matrix in addition to the small displacement stiffness matrix (linear analysis) allows the structure history and the effects of previous loadings on the internal stresses to be considered. This pre-stress state, that is omitted in linear analysis, modifies the global structure rigidity. The interest of the non-linear analysis on the biomechanical behaviour of simulated tree will be shown.