Assuming the theoretical perspective of Cognitive Linguistics, which is concerned with meaning in the language in use and considers metaphor and metonymy as phenomena of everyday language, this research examines metaphor and metonymy in legal texts. The aim of this work is to investigate the use of language in the legal textual production of the initial petition to understand the extent to which the proposal of conceptual metaphor and metonymy and the corresponding analysis methodology apply. In the investigation, two segments of initial petitions are selected, and 200 lexical units of content are analyzed. In the analysis, an adaptation of the Metaphor Identification Procedure - Vrije Universiteit (MIPVU) is applied to identify and classify metaphors and metonymies in the texts. We refer to dictionaries to present the contextual and basic meanings of each lexical unit and then establish the relationships built. The results show the relevance of use for establishing meaning, the need for a more comprehensive analysis methodology, and the prevalence of conventional and indirect metaphors, as well as metonymies by nominalization rather than deliberate uses, which is consistent with the literature in Cognitive Linguistics and with the specifics in the form, content, and style of the initial petition.