The time-dependent mechanical behaviour (TDMB) of softwood is relevant, e.g., when wood is used as building material where the mechanical properties must be predicted for decades ahead. The established mathematical models should be able to predict the time-dependent behaviour. However, these models are not always based on the actual physical processes causing time-dependent behaviour and the physical interpretation of their input parameters is difficult. The present study describes the TDMB of a softwood tissue and its individual tracheids. A model is constructed with a local coordinate system that follows the microfibril orientation in the S2 layer of the cell wall. The inclination of the local system to the global coordinate system reflects the microfibril angle of the tracheid. Normal excitations in the local system perform linear elastically, whereas shearing excitation in the local system produces both elastic and inelastic responses. The results of the model are compared with experimental results of different types. It was observed that the model is able to describe the results. Moreover, to some surprise, the introduction of only elastic and viscous properties on the microscopic scale leads to an apparent macroscopic viscoelasticity, i.e., the time-dependent processes are to a significant degree reversible.