Abstract This research objective of this collaborative research award is to break the barriers between the disciplines of geometric modeling and engineering analysis by placing engineering analysis of imprecise geometric models on a solid theoretical foundation and by developing the next generation of software tools based on the developed theory. Significant applications of this research, which cannot be handled by conventional methods, include analysis of unrepaired CAD models, reverse engineered or scanned models, models with small geometric features, toleranced models, and concept sketches. The research approach is based on treating imprecise models as families of geometric shapes, and on reformulating the problems of engineering analysis in terms of distances to the imprecise geometric boundaries. Specific deliverables of the research include theoretical foundations for the analysis of imprecise models, development of efficient geometric and numerical algorithms to support the theory, and implementation of prototypes demonstrating the efficacy of the obtained research results in the context of specific applications. If successful, the research will lead to significant advances in the field of computational engineering, resulting in a substantially wider adoption of the analysis tools throughout the product design cycle, as well as in emerging areas beyond engineering. Specific practical advances in interoperable systems will include analysis of early design concept models, constructed or acquired models with numerical errors, and detailed toleranced models. The results of this research have the potential to make a major impact on the educational curriculum, liberating students and practitioners from dealing with tedious data preparation and eliminating the need for unrealistic assumptions about the geometry.