The engineering response of fibrous soft soils, such as peats, is significantly influenced by the presence of fibres. Interpretation of laboratory tests performed on such soils is complicated due to the reinforcement provided by the fibres, which results in the material behaving as a composite, with properties different from traditional inorganic soils. The fibre matrix interaction complicates the estimation of geotechnical parameters such as shear strength and frictional properties from standard laboratory tests. Some empirical criteria to account for the contribution of fibres have been proposed, but there is no general consensus in practice. In this work, a numerical approach using finite element method and accounting for the kinematics of fibres is used to gain physical insights into the role of fibres in the mechanical behaviour of soft soils. Numerical replicas of common geotechnical laboratory tests were simulated as boundary value problems by superimposition of a soil matrix with a fibrous network. The contribution of fibres to the mechanical response of the soil sample is quantified for various stress and strain paths relevant to the engineering practice. The influence of two constitutive stress-strain relationships for the fibres upon stress reversal are compared and results suggest that fibres engage before they return to their original configuration, thus implying an influence of their compression history that could be linked to local tensioning of the fibres after compression. Further, laboratory tests on peat are used to validate the numerical approach, modelling the big fibres explicitly in the model and using an advanced model for the matrix, capable of reproducing behaviours such as distrotional hardening expected from the microscopic fibres in the matrix. The comparison highlights the effectiveness of the proposed numerical approach in accurately capturing the mechanical behaviour of natural fibrous peat as observed in laboratory tests. This approach provides valuable physical insights into the composite behaviour of peat. Furthermore, it offers a novel tool for interpreting extensive experimental data on peat samples, enabling the derivation of critical geotechnical parameters essential for the design and assessment of infrastructure founded on this unique soil.