Our paper aims with a discourse investigation tool: the model of argumentation proposed by the British philosopher Stephen Toulmin. Knowing the context of the emergence, the theoretical stakes, the analysis of the components and the evaluation of the effectiveness are necessary for a better understanding in the argumentative rhetorical analysis. On the one hand, we present a description of the six components: claim, data, warrant, backing, qualifier and rebuttal useful in the critical analysis of reasonings. On the other hand, we identify the presuppositions and provide a critical analysis of the advantages and limitations of the model in the research of practical argumentation in fields such as rhetoric, communication or critical thinking.