Modifying and hedging one's claims appropriately is an important characteristic of academic writing. This study focuses on the three main English modal verbs used to express "epistemic possibility" to avoid making strong statements, viz., "may", "might", and "could". The purpose of this corpus-based study is to explore modal verb usage by Japanese EFL undergraduate students and consider pedagogical implications of our findings. Our analysis suggests that the Japanese students' use of these modal verbs, especially "could", has a tendency to be informal and insufficiently academic. While the Japanese students use "could" very frequently, they do not use it sufficiently in the sense of "epistemic possibility", and some of their use is inappropriate not just in academic English but in English more generally. The observed high frequency of "could" may be related to topics and may also be due to the influence of L1. We discuss different factors that may explain the findings, based mainly on the overview of factors impacting on EFL learners' use of academic English offered by Gilquin and Paquot (2008). Too chatty: Learner academic writing and register variation. English Text Construction 1(1). 41--61), suggest several additions to this overview, and discuss implications for the instruction of these modal verbs in academic writing and in order to improve relevant teaching materials.