The rheology of fibre suspensions is a challenging subject in science and industrial applications; and has attracted considerable research effort for decades. This book is a detailed review of the authors' research work on this subject, and deals with some challenging problems, such as the fibre level simulation of non-dilute fibre suspensions in shear flow; the numerical simulation of complex fibre suspension flows and the simulation of particle motion in viscoelastic flows. All simulated results are in general agreement with experimental and other numerical results reported in the literature. This indicates that the numerical methods presented in this book are poerful tools able to solve difficult theoretical problems in the rheology of fibre suspensions. The numerical investigations shed new light on further understanding the relationship between the microstructure of fibres and the macro properties and flow behavioure of fibre suspensions. This book will be useful to researchers, graduate students and engineers, who are interested in composite material physics, polymer processing and rheology.