This descriptive study aims at analyzing the structures of 30 argumentative papers written by 30 foreign language university students, based on the adapted Toulmin (1958, 2003) model of argument structure comprised of six elements including (i.e., claim, data, counterargument claim, counterargument data, rebuttal claim, and rebuttal data).It also investigates how the uses of the Toulmin elements are related to the overall quality of argumentative papers written by Iranian B.A. students of English literature and what major problems students are struggling with in an EFL context. The Toulmin elements in the students’ papers were analyzed and the quality of papers was assessed. It was found that most of the Iranian EFL students’ argumentative papers participated in this study contained two basic elements of argument structures, namely, claims and data, but no paper presented the elements of counterargument claims, counterargument data, rebuttal claims, and rebuttal data. Potential implications of the findings are discussed as they pertain to EFL argumentative writing pedagogy expressing that the results are useful having some pedagogical implications regarding both writing assessment and teaching in EFL contexts also paving the way for future research in this regard.