Flexible pulp fibres produce paper of higher quality than their stiff counterparts. The pulp and paper industry has a keen interest to measure fibre flexibility and to fractionate fibres based on flexibility. The objective of this thesis is to theoretically study the static and dynamic behaviour of pulp fibres with direct applications to fibre flexibility measurement devices and fibre screening. Governing equations, which represent the deflection and motion of pulp fibres, are developed and numerical methods are utilized to solve the mathematical formulations. Static large deflection beam theory is applied to the geometry of four existing fibre flexibility measurement devices to determine the advantages and shortcomings of each method. It is shown that the small deflection analysis predicts flexibility with an error of less than 10% when compared to the large deflection analysis for fibre deflections of less than 20% of the span length. Furthermore, it is concluded that a better estimate of the hydrodynamic forces acting on the pulp fibres is required. To study the behaviour of flexible fibres in pulp screening applications, non-linear equations representing the motion of a flexible fibre are developed. Two methods to represent the dynamic interaction of a fibre with the flow domain walls are proposed. Together with a Computational Fluid Dynamics (CFD) analysis, the motion of fibres in a channel flow with a slot are studied and the effect of fibre flexibility on the ability of the fibres to pass through the slot is examined. For the first time, a theoretical model has been used to show that screening based on fibre flexibility does occur. However, it is shown that the predominant property which governs the fractionation of fibres is the fibre length. To propose a direct method to model the flow of a flexible fibre for future applications and a method to predict the hydrodynamic forces acting on a fibre, an automatic three-dimensional finite element mesh generating algorithm, based on the Delaunay triangulation, is developed for use with CFD software. A unique method of mesh refinement is defined and it is shown that the method is extremely efficient for typical fibre geometries.