The objective of the present study is to analyze the appellative function implementation within the political discourse on the basis of speech transcripts of D. Trump's and H. Clinton's speeches of both election and post-election periods. The selected data is analyzed as a social phenomenon in relation to the discourse analysis; the frames that are resorted to by the politicians are investigated from the perspective of the cognitive analysis, and most regular stylistic devices are considered via the rhetoric analysis. By analyzing the appellative function from different perspectives we consider the tools the politicians use to achieve one main goal; that is getting the people to vote for the speaker. Research on the appellative function on the basis of the US election 2016 is greatly valuable from the linguistic point of view, as the candidates represent quite contrasting communicative styles and framing models. Thus, implementation of the appellative function contrasts in Clinton's and Trump's rally speeches as they refer to the opposing cognitive models- Nurturant Parent mоdel and Strict Father model respectively. In order to to carry out the research of language means that constitute the appellative function within the post-election period, we undertook the comparative analysis of the personal pronouns, repetition and modality. It should be also highlighted, despite the simple speech surface, Trump selects the words and frames deliberately to enhance the appellativenes of his speeches. Trump's sentences are shorter and not so sophisticated as Clinton's ones, hence quickness, decisiveness and speed characterize his claims. The study reaches a conclusion that exercising power and maintaining solidarity with the listeners is correlated to some extant with the ways appellative function is realized in the speeches. The practicаl significаnce is that the results of the thesis may be successfully used in the university courses of American SocioCultural Linguistics, as well as in the special courses on political studies.