This paper describes an automated approach to deform an analysis mesh applied to a computer-aided design (CAD) model in response to a change in the shape of the CAD model. The process has been used to overcome a key issue that occurs during the shape optimization process. It is an advance over existing techniques because it works even when the boundary topology of the CAD model changes during the shape change, which other approaches cannot generally accommodate. To achieve the deformation, an analysis topology representation is created for each model, such that there is a one-to-one mapping between the analysis topology representing the models before and after the shape change. Strategies are presented to parameterize the superset entities in the analysis topology that have no global mathematical definition. The surface mesh is deformed in a way that allows the underlying surface/edge parameterizations to change, and it is shown how the domain mesh can be updated based on the surface mesh deformation. If the models before and after shape change have the same genus, then a small dimensional change in the shape of the model will result in meshes with the same topology, even if the topology of the underlying CAD representation has changed. This is highly desirable when evaluating sensitivities to a design change during an optimization.