Anisotropy and viscoelasticity are key characteristics of soft materials, particularly in biological tissues and engineered composites with fibrous microstructures. These materials often exhibit complex mechanical behaviour due to the spatial distribution of fibres, introducing challenges in accurately modelling their nonlinear viscoelastic response. In this study, building upon a previously developed theoretical model, we investigate how fibre distribution and characteristic time scales affect stress relaxation in anisotropic viscoelastic materials undergoing large deformations. Using a computational model and a variational formulation of the viscoelastic framework, we perform a series of numerical simulations encompassing uniaxial and simple shear tests. Our findings demonstrate that fibre dispersion and orientation strongly shape the stress relaxation response in uniaxial tests, and we identify a specific fibre angle where relaxation becomes independent of fibre dispersion. Additionally, the results from shear tests reveal the impact of anisotropic relaxation times on the dynamics of shear and normal stresses. This study enhances our understanding of the interaction between fibre distribution and viscoelasticity, with potential implications for design and experimental characterization of soft materials.