This study investigates research writing anxiety and self-efficacy beliefs among English-as-a-Foreign-Language (EFL) graduate students in engineering-related fields. The relationship between the two writing affective constructs was examined and students' perspectives on research writing anxiety were also explored. A total of 218 survey responses from engineering graduate students at Taiwanese universities were analyzed, along with qualitative data from open-ended questions and semi-structured interviews. The findings show that while master's and doctoral students felt a similar moderate level of writing anxiety, senior doctoral students were more self-efficacious about writing research papers in English than their junior counterparts. Overall, students with higher writing self-efficacy felt less apprehensive. Additionally, among the individual variables, experience in writing for publication better predicted writing anxiety and self-efficacy than students' self-reported English proficiency and the number of writing courses taken. The qualitative findings indicated various sources of graduate-level writing anxiety, including insufficient writing skills in English, time constraints, and fear of negative comments. Furthermore, composing different sections of a research paper provoked different levels of anxiety due to the variations in the rhetorical purposes and discourse structures of particular sections. Implications on dealing with research writing anxiety are also discussed.