Particularly in object-oriented design methods, design patterns are becoming increasingly popular as a way of identifying and abstracting the key aspects of commonly occurring design structures. The abstractness of the patterns means that they can be applied in many different domains, which makes them a valuable basis for reusable object-oriented design and hence for helping designers achieve more effective results. However, the standard literature on patterns invariably describes them informally, generally using natural language together with some sort of graphical notation, which makes it very difficult to give any meaningful certification that the patterns have been applied consistently and correctly in a design. In this paper, we describe a formal model of object-oriented design and design patterns which can be used to demonstrate that a particular design conforms to a given pattern, and we illustrate using an example how this can be done. The formality of the model can also help to resolve ambiguities and incompletenesses in the informal descriptions of the patterns.