Most conventional quantitative information processing oriented design support techniques are difficult to use for conceptual design because product information available at this design stage is mainly incomplete and qualitative. The description of shapes is the core of mechanical product models. Although many shape modelling methods have been proposed for the automation of downstream design tasks and the integration of design and manufacturing, most of them seen inadequate for conceptual design support. In this paper and its continuation we describe a new approach to shape modelling, called qualitative solid modelling. In the current report, we first investigate problems in the conventional shape modelling methods. Then, a new method is proposed for representing solid shapes based on qualitative spatial relations that are defined by extending the temporal interval relations given by J.F.Allen in his temporal logic(6). A qualitative solid model is a domain network which has domains that are cuboids as its nodes and qualitative spatial relations among them as its links. Because an ordinary domain network with many domains is considerably large, a method for organizing domain networks to control their scales has been formalized and realized.