Flax (Linum usitatissimum L.) is a plant of industrial interest. Its fibres have traditionally been used for textile applications and more recently, for composite reinforcement. To increase fibre yields, varietal selection has been used to develop varieties having high fibre content while retaining good resistance to lodging. This selection process has led to impressively slender structures of flax compared to other herbaceous plants. The present study focuses on the mechanical stability of flax related to its specific architecture. An anatomical study of transverse sections provides information about the architecture of flax stems, including the repartition of the internal reinforcing tissues being phloem fibres and xylem. Then, by using three-point bending tests, flexural modulus is evaluated along the stem. The safety factor (SF) against buckling for the plant was estimated based on Greenhill's model, taking into account gradients in diameter, load, and elastic modulus. Although flax plants have an unusually slender structure, they are mechanically stable. The stability of the plant is ensured by a high stem flexural modulus. This originates from an external ring composed of high-performance fibres, while an inner thick porous xylem provides the plant with a high resistance to local buckling. This is useful information for breeders, demonstrating that it is possible to keep increasing fibre yield without jeopardising plant stability.