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Paper can be regarded as a network of cellulosic fibres, especially at lower basis weights. When the elastic behaviour of paper sheets is modelled, it is normally essential to know or to assume how the stresses (and strains) are distributed at the fibre level. This article presents an attempt to estimate how the stresses are transferred throughout a simple fibre network using the finite element method (FEM). Attention is mainly focused on the axial fibre stress distribution when the network is uniaxially deformed. The presence of fibre ends is found to induce local stress increases (“stress concentrations”) in the deformed network, which presumably have a bearing on the ultimate properties of the sheet. The influence of the properties of the bonds between crossing fibres on the mechanical properties is also investigated. It is noted that the bond stiffness has no significant effect on the stress transfer between fibres provided that the stiffness is above a critical value. Below this value the stress transfer deteriorates rapidly.