The increase in marine traffic has resulted in the need for traffic routing schemes in areas of high vessel density. In order to assess the viability of a scheme before it is brought into use a simulation study can be used. This thesis describes the construction of a computer model to simulate the behaviour of mariners using the concepts of domains and arenas to control their actions. The arena is an area around a ship where one navigator takes account of another ship's presence. The domain is the area around his ship which a navigator wishes to keep clear of other vessels and stationary objects. The model is validated against data gathered in the Dover Strait from the coastguard radar station at St. Margaret's Bay and from experiments conducted in a radar training simulator. The model is shown to produce realistic results for vessels overtaking one another and for vessels meeting with a collision risk 96 per cent of situations can be realistically simulated.