The stems of flax (Linum usitatissimum L. cv. 'Mogilevsky') contain many gelatinous fibers in their phloem. These fibers are important for the mechanical stability of the plant as well as for industrial applications. Gelatinous fibers are known to have a motor function in the xylem of trees and in many plant organs. This function arises from the so-called maturation strain, i.e., the tendency of the gelatinous layer to shrink during fiber maturation, resulting in a state of residual tensile stress. However, the occurrence of tensile maturation strain in flax phloem fibers remains to be demonstrated, and its magnitude has never been evaluated. Here we present a novel method to highlight and quantify this strain. The method consists in splitting a stem segment longitudinally, and measuring the curvature of the half segments through their opening distance. By using a mechanical model, the maturation strain can be calculated from the curvature, the dimensions of the component tissues, and their elastic properties. The model is validated by the agreement between model predictions and observations. The splitting experiment provides qualitative evidence that flax phloem develops tensile stress during maturation, just as xylem gelatinous fibers do. Calculations enable quantitative estimation of the maturation strain. The magnitude of this strain for the material studied is, on average, -1.5%.