Analyzing discourses can shed light on language as a social semiotic system, the construction of identity and the operations of ideology and power. The purpose of this study is twofold. Firstly, it aims to unveil Thai fourth-year English-major students' utilization of lexical choices with connotations that enact the identities of the Baan Nontapum Foundation (BNF) or Home for Children with Disabilities, in their website project. Secondly, the study was conducted to further explore how and why those discursive strategies were utilized to construe the BNF and disability identities through the participants' lexical selection. In this study, the social model of disability, which views disability as a form of social oppression, in combination with Fairclough's Critical Discourse Analysis was used as the theoretical framework for analyzing the participants' language use on their self-designed websites. The analysis revealed the participants' utilization of different lexical choices with connotations to presuppose the BNF's identity as a 'warm,' 'effective,' and 'altruistic' organization that provides various forms of special care to their children and children with disabilities' identities as 'socially independent' and 'capable of becoming self-supporting.' However, the notions of 'social exclusion' and 'lack of social collaboration' were found to be embedded in the discursive reproduction of the discourse.