<p>Since Darwin, the study of climbing plants on a cylindrical support has been the subject of numerous articles in plant biology, mechanics and soft robotics. One way to study the winding of an elastic plant stem is to consider the growth of the plant stem. However, as the development of stems takes place over a long period of time, a static study can also be considered. For a simple analysis, a static approach requires taking into account elasticity, gravitational forces and turgor pressure. The objective of our calculations is to present a simplified model demonstrating that plant stems generally climb their cylindrical supports by taking the form of a helix. Using the Frenet-Serret reference frame, we consider a solid deformation of thin plant stems. In our calculation, no complex biochemical processes are considered. In the literature, they have been used to study the chirality of the helix formed by the rods. Here, we are simply using the principle of minimum energy. Compared to elastic energy, the effect of gravity and turgor pressure can often be neglected. Finally, it is demonstrated that the diameter of the support plays an important role in the climbing of thin plant stems.</p>