In this thesis it is suggested that the cost-effectiveness of road safety expenditure on low cost engineering remedial works could be improved because the currently adopted methods for assessing expenditure priorities do not necessarily identify thosa sites at which the greatest potential for accident reduction exists. An alternative method for the generation of more cost-effective programmes of works is proposed and justified. This method adopts the rationale of identifying those sites at which accidents are occurring in higher numbers than would otherwise be expected for such sites with equivalent traffic volumes and locations. The justification for the method involves detailed statistical analyses of over 10,000 accidents occurring in Lothian Region for the years 1979-1982 which demonstrate that there are significant relationships between accidents and traffic volumes and location details (eg junction type, form of junction control, adjacent roadside development and carriageway type). On this basis, models for accident occurrence have been determined. The analyses show that the temporal distribution conforms with a Poisson process and that the spatial distribution is negative binomial. It is shown - for both links and junctions - that whilst there are significant differences between the models for different accident types, they do not, in aggregate, produce significantly better models for all accidents than simple all accident models. In addition, the importance of regression-to-mean has been established as an effect which should be accounted for not just at the monitoring stage of completed schemes but as an integral part of the initial site selection process. Finally, it is demonstrated that the proposed method, which is called Potential Accident Reduction (PAR), may provide an improvernent of cost-effectiveness of road safety expenditure of up to 25% over the currently adopted methods.