The failure of oil well drillstrings due to torsional and longitudinal stresses caused by stick-slip phenomena during the drilling operation causes great expense to industry. Due to the complicated and harsh drilling environment, modelling of the drillstring becomes an essential requirement in studies. Currently, this is achieved by modelling the drillstring as a torsional lumped model (which ignores the length of the drillstring) for real-time measurement and control. In this thesis, a distributed-lumped model including the effects of drillstring length was developed to represent the drillstring, and was used to simulate stick-slip vibration. The model was developed with increasing levels of detail and the resultant models were validated against typical measured signals from the published literature. The stick-slip model describes the friction model that exists between the cutting tool and the rock. Based on theoretical analysis and mathematical formulation an efficient and adaptable model was created which was then used in the application of a method of species conserving genetic algorithm (SCGA) to optimise the drilling parameters. In conclusion, it was shown that the distributed-lumped model showed improved detail in predicting the transient response and demonstrated the importance of including the drillstring length. Predicting the response of different parameters along the drillstring is now possible and this showed the significant effect of modelling the drillcollar. The model was shown to better represent real system and was therefore far more suited to use with real time measurements. / Iraqi Government, Ministry of Higher Education and Scientific Research.