Fibrous soft tissues such as skin, tendons and ligaments are vital to the normal function of mammalian bodies. These soft tissues are complex materials: they exhibit anisotropy, nonlinearity and viscoelasticity. To the best of our understanding, a soft tissue’s microstructure – its constituents and their arrangement within the tissue – causes these complex behaviours. The microstructural modelling of soft tissues is, therefore, an important area of research into understanding the stresses and strains acting on a soft tissue, physiologically and non-physiologically (e.g. in surgery), and possibly, in the distant future, creating replacement tissues that can adequately replicate normal tissue behaviour. Consequently, we shall propose a new microstructural model of soft tissue deformation, fit the model to four experimental data sets of uniaxial tensile testing and compare the fits to two pre-existing models of soft tissue behaviour.