Peat is an organic material which presents significant challenges in environmental and geotechnical engineering due to its hydrological importance and unconventional mechanical behaviour. Its complex hydro-mechanical response arises from its highly porous, compressible and anisotropic fabric, composed primarily of vegetal fibres at varying decomposition stages. This multiscale fabric enables peat to sustain large shear stress ratios at the expense of very large strains. While recent decades have seen advancements in the mechanistic understanding of peat behaviour, current models struggle to capture the mechanical contribution of large fibres while accounting for their reorientation and interaction with the matrix under large deformations. This study addresses this limitation by introducing a numerical framework rooted in large strain mechanics to model peat as a composite material, allowing for fibre rotation and volumetric variation during loading. Peat is conceptualised as a two-phase composite of large elastic fibres acting as kinematic restraints embedded within an elastic-plastic matrix of small fibre aggregations. Fibre geometry is parameterised using experimentally derived distributions, and a novel function is introduced to represent fibre orientation. Mechanical properties of the fibres were estimated from experimental tests and incorporated into the model using a statistical fracture mechanics framework. The matrix behaviour is modelled with existing constitutive relations for reconstituted peat. The proposed model demonstrates quantitative agreement with experimental data from triaxial compression and extension tests. It underscores the role of fibre kinematics in shaping the stress-strain response, particularly in enabling sustained hardening above the critical stress ratio of the matrix while retaining the features of excess pore pressure generation. The results emphasise that the complex interaction between fibres and matrix requires multiscale modelling and accurate representation of all constituents. This work offers a promising framework for predicting peat mechanical behaviour and provides a foundation for developing simplified constitutive models and exploring additional physical couplings.