The paper presents the Petri net ontology that should enable sharing Petri nets on the Semantic Web. Previous work on formal methods for representing Petri nets mainly defines tool-specific Petri net descriptions (i.e. metamodels) or formats for Petri net model interchange (i.e. syntax). However, such efforts do not provide a suitable model description for using Petri nets on the Semantic Web. This paper uses the Petri net UML model as a starting point for implementing the Petri net ontology. The UML model is then refined using the Protégé ontology development tool and the Ontology UML profile. Resulting Petri net models are represented on the Semantic Web is using XML-based ontology representation languages, Resource Description Framework (RDF) and Web Ontology Language (OWL). We implemented a Petri net software tool as well as tools for the Petri net Semantic Web infrastructure.