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.