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The three-dimensional geometry of a building is a vital prerequisite for Building Information Modeling. This chapter examines the principles involved in representing geometry with a computer. It details explicit and implicit approaches to describing volumetric models as well as the basic principles of parametric modeling for creating flexible, adaptable models. The chapter concludes with an examination of freeform curves and surfaces and their underlying mathematical description. Geometric modeling in the context of BIMA Building Information Model contains all the relevant information needed for the planning, construction and operation of a building. The three-dimensional description of the geometry of a building is one of the most important aspects without which many BIM applications would not be possible. The availability of a model in three dimensions offers significant advantages over conventionally drawn plans:• The planning and construction of the building can be undertaken using a 3D model rather than separate plans and sections. Drawings are then generated from the 3D model, ensuring that the separate drawings always correspond and remain consistent with one another. This almost entirely eradicates a common source of errors, especially when alterations are made to the plans. But a three-dimensional geometric model on its own is not sufficient for generating plans that conform