In this paper we lay the foundations for exchanging, adapting, and interoperating engineering analysis models (EAMs). Our primary foundation is based upon the concept that engineering analysis models are knowledge-based abstractions of physical systems, and therefore knowledge sharing is the key to exchanging, adapting, and interoperating EAMs within or across organizations. To enable robust knowledge sharing, we propose a formal set of ontologies for classifying analysis modeling knowledge. To this end, the fundamental concepts that form the basis of all engineering analysis models are identified, described, and typed for implementation into a computational environment. This generic engineering analysis modeling ontology is extended to include distinct analysis subclasses. We discuss extension of the generic engineering analysis modeling class for two common analysis subclasses: continuum-based finite element models and lumped parameter or discrete analysis models. To illustrate how formal ontologies of engineering analysis modeling knowledge might facilitate knowledge exchange and improve reuse, adaptability, and interoperability of analysis models, we have developed a prototype engineering analysis modeling knowledge base, called ON-TEAM, based on our proposed ontologies. An industrial application is used to instantiate the ON-TEAM knowledge base and illustrate how such a system might improve the ability of organizations to efficiently exchange, adapt, and interoperate analysis models within a computer-based engineering environment. We have chosen Java as our implementation language for ON-TEAM so that we can fully exploit object-oriented technology, such as object inspection and the use of metaclasses and metaobjects, to operate on the knowledge base to perform a variety of tasks, such as knowledge inspection, editing, maintenance, model diagnosis, customized report generation of analysis models, model selection, automated customization of the knowledge interface based on the user expertise level, and interoperability assessment of distinct analysis models.