The relevance of context has been acknowledged also recently as a fundamental element for the correct evaluation of argumentative moves within institutional fields of interaction. Indeed, not considering the larger culture-specific and social features of the context within which the interactions take place poses problems of interpretation of the data and comparability of results. Starting from these considerations, the paper aims at discussing a model for the description of the social context of interaction that may allow for a better interpretation and evaluation of argumentative moves within medical consultations. The efficacy of the model is shown by applying it to the description and analysis of examples of real-life consultations recorded in the Italian region of Lombardy. In the first section, the model for the description of the social context of interaction is presented and discussed. In the second section, examples of argumentative passages from a selection of consultations are presented and commented on by relying on the model. Some concluding remarks and further developments of the research are proposed in the final section.