The use of plant fibres as reinforcements in engineering applications requires reliable determination of their mechanical properties. This work focuses on single-fibre longitudinal tensile testing and the significance of the tensile system compliance for obtaining reliable results. Four types of fibre are tested, namely basalt, aramid, elementary flax fibres and flax fibre bundles. An automated laser scanning method is used to determine their cross-sectional area (CSA) based on circular and elliptical morphological models. The compliance of the tensile system is evaluated by standard and photomechanical analyses, and its influence on the assessment of mechanical properties of the fibres is discussed. Our results show that the evaluation of the compliance is highly dependent on fibre type, but also on the choice of CSA morphological model. The resulting correction on maximum tensile moduli ranges from 6.5 % to 37.6 % for small-diameter fibres, and can reach 55.1 % for large-diameter fibres as flax fibre bundles. Moreover, we evidence that the tensile system compliance is not necessarily constant and evolves with the force range covered during the tensile test. This can have a significant impact on the shape of the stress-strain curves, and hence on the analysis of the overall mechanical behaviour of the fibres.