The thesis deals with the simulation and optimisation of parts of the Lyocell process. Starting with trees and ending with cellulose fibres, the Lyocell process is one of the most advanced methods for creating natural fibres without causing any pollution to the environment. In particular, the filter systems and the spinneret at the end of the spinning process are studied in detail. After locating the key players that prohibit the spinneret to function continuously, possible blocking theories are described. Using the possibilities of Computational Fluid Dynamics (CFD), these theories are than verified using computer simulations. Finally, after studying the optimisation potential, the filters and spinneret are optimised using a variational method. A very complex and highly advanced industrial process has been investigated intensively from various angles while at the same time, solid suggestions on improvements are given.