A new descriptive formalism is introduced to represent the state of a bonded random network of fibres, such as paper, when subjected to mechanical deformation. Energy is considered to be distributed among the lengths of free fibre between inter-fibre bonds and a criterion for the fracture of these bonds is postulated. The theory is used in the present paper to derive the cumulative fracture of bonds as a function of time in a network which suffers a uniform rate of elongation. Good agreement was obtained with experimental recordings of the failure of bonds in a thin sheet of paper. No systematic influence of the rate of straining on the mode of bond failure was detected.