We propose a minimum input mechanical model of pulp fibres. A pulp fibre can be idealised as a complex compound bar, microfibrils render its behaviour anisotropic. The objective of this work is twofold: (i) develop an anisotropic viscoelastic material model of a pulp fibre that shows the essential characteristics with a minimum number of material parameters and (ii) establish suitable experiments with pulp fibres for obtaining these parameters. The model consists of an additive combination of elastic potentials for an isotropic and an anisotropic part. Viscoelasticity is implemented by a generalised Maxwell model. We suggest an incompressible treatment of the material to relate experiments and material parameters in a well-defined manner. By this means, the calibration of the parameters is performed with only two micromechanical experiments, atomic force microscopy nanoindentation on the fibre's surface and uniaxial tensile tests. We advocate this strategy for certain applications, such as in paper network simulations or fibres in a dry state, when the fibre's compressibility is of minor importance. The results of this analysis show a good performance of the proposed model applied to pulp fibres.