The external shape and internal lumen of flax fibres are investigated using X-ray microtomography (mu-CT) and finite element (FE) modelling. mu-CT reveals an intricate flax fibre and lumen morphology, with mean porosity contents between 0 and 7.2%. The FE model is based on 3D volumes obtained by X-ray mu-CT and tensile testing in the elastic domain. Numerical results demonstrate the decrease of stiffness as a combined effect of porosity and stress heterogeneity triggered by geometrical considerations. Moreover, stress concentrations induced by both surface roughness and complex lumen shape were observed, highlighting their possible implication in failure mechanisms. However, Young's moduli are overestimated compared to experimental curves and non-linearities are not considered by the rather strong hypothesis of this model (linear elastic material: no viscosity, plasticity or damage mechanisms taken into account). Future work should include the orientation and reorientation of cellulose microfibrils upon tensile testing, as well as damage mechanisms.