This volume presents papers from the Third Conference on Computational Models of Argument, held in September 2010 in Desanzano del Garda, Italy. Argumentation has been the subject of research in a number of different fields where a solution is sought for the many problems encountered in the knowledge representation and reasoning area of artificial intelligence. The goal is the development of applications using strategies akin to the commonsense approach applied by humans. In recent years such practical applications of basic research results have been the subject of increasing attention, especia.