This paper gives the Petri net ontology as the most important element in providing Petri net support for the Semantic Web. Available Petri net formal descriptions are: metamodels, UML profiles, ontologies and syntax. Metamodels are useful, but their main purpose is for Petri net tools. Although the current Petri-net community effort Petri Net Markup Language (PNML) is XML-based, it lacks a precise definition of semantics. Existing Petri net ontologies are partial solutions specialized for a specific problem. In order to show current Petri net model sharing features we use P3 tool that uses PNML/XSLT-based approach for model sharing. This paper suggests developing the Petri net ontology to represent semantics appropriately. This Petri net ontology is described using UML, Resource Description Framework (Schema) – RDF(S) and the Web Ontology Language – OWL.