AbstractRisk engineering models for decision making under uncertainty are illustrated by a succession of increasingly complex example applications. The approach is based upon simple arithmetic procedures which are easy to understand and use. Offshore North Sea projects are the basis for the example applications, but the approach has been used in a range of problem environments in the U.K., Canada and U.S.A. The emphasis is a flexible structure for viewing problems which allows modelling at a level of detail and with a degree of quantification tailored to the needs of the context. The concern is gaining useful insight, not model solution optimisation.