This work aims to model the mechanical processes used by tree branches to control their posture despite their increasing weight loading. The two known options for a branch to maintain its orientation are the asymmetry of maturation stress, including reaction wood formation, and eccentric radial growth. Both options can be observed in nature and influence the stress distribution developed in the branch each year. This so-called "growth stress" reflects the mechanical state of the branch. In this work, a growth stress model was developed at the cross-section level in order to quantify and study the bio-mechanical impact of each process. For illustration, this model was applied to branches of two 50-year-old trees, one softwood \textit{Pinus pinaster} and one hardwood Prunus avium, both simulated with the AMAPSim finite element software. The computed outputs enlightened that, for both Prunus avium and Pinus pinaster, eccentric radial growth is less efficient than the formation of reaction wood to counter increasing gravity stress applied to the branch. For the pine, although eccentric growth does not necessarily act as a relevant lever for postural control, it greatly modifies the profile pattern of mechanical stress and could provide mechanical safety of the branch. This work opens experimental perspectives to understand the biomechanical processes involved in the formation of branches and their mechanical safety.