The publication rate of Indonesian academics in reputable international journals is far below those of neighbouring countries. This is because Indonesian academics are not familiar with the appropriate rhetorical style of English research articles although they can write academic texts in English reasonably well. This study investigated the rhetorical problems experienced by Indonesian lecturers in social sciences and humanities when writing research articles for international journals. In this study, all sections (abstract, introduction, methods, results and discussion) of research article drafts written by Indonesian academics were analysed based on their rhetorical styles following the models suggested by Swales (1990, 2004), Swales and Feak (2009), Lim (2006), and Peacock (2011). The results show that Indonesian authors have significant rhetorical problems in writing the introduction, results and discussion sections but few problems with writing abstracts and the methods section. The majority of these academics fail to write a convincingly argumentative introduction and discussion because they either do not use relevant references at all or they use them in improper ways. The study concludes that Indonesian authors must learn the ideal rhetorical styles of research article introductions and discussions, especially the use of references, in order to be accepted in international journals.