Abstract: In software-based generative design, a user specifies goals expressed as objectives and constraints to a software application and the application returns a set of feasible and/or optimal design solutions. For problems involving discrete design variables, such as in configuration design, searching the design space is often computationally intractable. Therefore, in the context of the configuration design of mechanical assemblies, we are investigating the use of ontologies to model and reason about designs while providing the ability to more efficiently prune infeasible designs. In this paper, we present an ontology to specify connection, parthood, and shapes in mechanical assemblies, so that the constraints of feasible configurations can be logically expressed and used during generative design. The ontology extends the Ground Mereotopology (MT) of Casati and Varzi to a multi-dimensional mereotopology and combines it with a qualitative shape ontology based on the Hilbert’s axiomatic theory of geometry. Relationships between equi-dimensional individuals are captured by MT, while individuals with different dimensions are mereotopologically independent and are related by incidence relations. The proposed ontology is a module in the larger effort to develop an overarching PhysicalWorld Ontology. We demonstrate the application of the proposed ontology in specifying properties of suspension systems and mechanical joints.