Flax fibres are employed in various applications such as non-wovens, fibre-reinforced composites and other bio-based materials. Owing to their biological origin, they exhibit pronounced natural variability in geometry, microstructure and defect content, which translates into variability in mechanical response. From a mechanics standpoint, an individual flax fibre can therefore be viewed as a complex, hierarchically organised compound that exhibits effective transversely isotropic behaviour arising from its multi-scale architecture. In this work, cyclic tensile experiments were performed on single flax fibres, and the mechanical response was characterised in terms of stress-strain curves. The tests were repeated for several loading rates in order to quantify rate-dependent effects and changes in stiffness during repeated loading and unloading. Key features such as hysteresis, apparent stiffness evolution and irreversible strain accumulation were identified and used as target characteristics for subsequent constitutive modelling. We aim to formulate a constitutive model that reproduces the features of the measured stress-strain response. We build on our earlier rate-independent formulation [1] combining orthotropic elasticity and orthotropic plasticity in a finite-strain hyper-elasto-plastic framework that employs a covariant approach [2,3] in which plastic deformation drives the evolution of orthotropy. The resulting constitutive equations capture deformation-induced changes in material symmetry, conceptually related to plastic spin, and enable modelling of the observed stiffness increase. In this work, the framework is further extended to include rate effects via viscous contributions in both visco-elasticity and visco-plasticity. The numerical simulations show very good agreement with the experimentally obtained stress-strain curves across the investigated loading rates. [1] C.C. Celigoj, M.H. Ulz, J. Mech. Phys. Solids, Vol. 193, 105846, 2024, doi:10.1016/j.jmps.2024.105846. [2] J. Lu, P. Papadopoulos, Comput. Meth. Appl. Mech. Eng., Vol. 193, pp. 5339–5358, 2004, doi:10.1016/j.cma.2004.01.413040. [3] M.H. Ulz, C.C. Celigoj, Comput. Meth. Appl. Mech. Eng., Vol. 401, 115567, 2022, doi:10.1016/j.cma.2022.115567.