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, especially within the autonomous agents and multiagent systems community. To answer the need for a forum where advances in the field could be discussed in a specialised manner by members of the argumentation community, the first conference in this series was held in 2006 at the University of Liverpool. The success of both the first and the subsequent second conference, held in Toulouse in 2008, has established this conference as a biennial event. The call for papers for the third conference resulted in the submission of 67 papers, of which the 35 full papers and five short papers selected are presented here, along with two invited papers from prof. Gerhard Brewka and prof. Douglas Walton. Subjects covered range from formal models of argumentation and the relevant theoretical questions, through algorithms and computational complexity issues, to the use of argumentation in several application domains. Overall this volume provides an up to date view of this important research field and will be of interest to all those involved in the use and development of artificial intelligence systems.