The article deals with the problem of the methodology of designing computer ontology of the subject discipline by the future teachers-engineers in the field of computer technologies. The scheme of ontology of the subject discipline is presented in which the set of concepts of the future computer ontology and the set of relations between them are represented. The main criteria of the choice of systems of computer ontologies for designing computer ontology of the subject discipline: software architecture and tools development; interoperability; intuitive interface are established. The selection of techniques for designing ontologies using computer ontology systems is carried out. The algorithm of designing computer ontology of the subject discipline by the future teachers-engineers in the field of computer technologies is proposed.