Based on the analysis of the connotations of the competitiveness and their relationships, the mapping relationships among four elements of the competitiveness, i.e. connection, resource, ability, knowledge, the concrete behaving forms of the firm competitiveness, i.e. product, sale, capital, brand, and the 4 competition abilities of a supply chain, i.e. system, organization, technique, cognizing are discussed. A polyhedron structure of the competitiveness is proposed. Based on the various competitiveness theories published,several theoretical analysis paradigms are concluded, including competition environment paradigm, market competition balance paradigm and the ability- based firm competition paradigm.