This paper presents a spatio-temporal model coupling tree growth and tree biomechanics. This model takes the form of partial differential equations. Different numerical methods have been implemented and compared' in order to integrate the model equations at the branch scale. The model takes into account the three main components involved in the tropism of lignified axes, namely the primary reorientation of the branch tip, the stiffness increase due to secondary growth and the secondary reorientation involved by a differential in cell maturation strains. Simulation results are shown to demonstrate the capacities of the model to simulate realistic stem/branch motions.