Design support systems need to be developed on the basis of an understanding of the human design process to be useful during design. The explicit representation of design history and rationale are of particular importance for explanation and reuse. Within the DESIRE framework for compositional modelling, a generic task model of design has been developed that clearly specifies the role of design history and design rationale within the design process. The model provides a structure to distinguish different types of design rationale, according to the functional role they play in the design process. It has been used to structure the modelling process of an example aircraft design task, which illustrates the various instances of design rationale that can be generated.