This thesis investigates the feasibility of developing a mathematical model to provide quantitative measures of total ship safety. Safety is an intuitive concept and is a subset of economic utility. There is economic pressure to transport goods at minimum cost and, without regulation, the frequency of shipping casualties could be unacceptably high. Mathematical methods associated with elements that influence ship safety are reviewed. Techniques for analysing ships' structures, stability, motions and engineering reliability are well established, but those for assessing the effect of human involvement, and operational and organisational influences on safety are less developed Data are available for winds, waves, currents and tidal movements, and their variability suggests that probabilistic models are appropriate Given the complexity of the international shipping industry, a simple computer model is developed in which 50 ships serve four ports. This allows safety to be assessed when input variables are adjusted. Obstacles to developing a mathematical model of ship safety are identified, and it is concluded that the feasibility of such a model depends on its required inclusiveness and utility.