The coconut palm (Cocos nucifera L.) stem tissue (referred to as cocowood in this study) is a complex fibrovascular system that is made up of fibrovascular bundles embedded into a parenchymatous ground tissue. The complex configuration of fibrovascular bundles along with the non-uniform distribution of the material properties likely allow senile coconut stems to optimize their biomechanical performance per unit mass (i.e., mechanical efficiency) and grow into tall, slender, and very flexible plants with minimum resources of biomass and water. For the first time, to the best of the authors' knowledge, this paper examines, from the integral (i.e., stem structure) and macroscopic (i.e., tissue structure) levels of hierarchy, the characteristic triple helix formation depicted by the fibrovascular bundles within the monocotyledon cocowood. The natural course of the tangential orientation of the axial fibrovascular bundles is mapped for the whole cocowood structure by quantifying 264 cocowood discs, corresponding to 41 senile coconut palms estimated to be >70 years old. The observed variations were modeled in this paper by simple equations that partially enabled characterization of the cocowood fibrovascular tissue system. Furthermore, 11 finite element analyses (FEA) were performed over a three dimensional (3D) finite element (FE) model resembling a characteristic coconut palm stem of 25 m in height to analyze the biomaterial reactions produced by the progressive deviation of the tangential fibrovascular bundles on the cocowood mechanical response (i.e., on the material compressive strength and the bending stiffness). The analyses in this study were carried out for the critical wind speed of 23 m/s (i.e., Gale tornado according to the Fujita tornado scale). For each analysis, the characteristic average maxima degree of orientation of the cocowood fibrovascular bundles was varied from 0° to 51°. The acquired results provided a deep understanding of the cocowood optimum fibrovascular tissue system that denotes the natural evolution of the material through millions of years. The knowledge advanced from this study may also serve as concept generators for innovative biomimetic applications to improve current engineered wood products.