Critical thinking is a key transversal competency of the 21st century, but some students have difficulty, especially during the transition to online learning due to the COVID-19 pandemic. This study aims to identify epistemological obstacles in critical thinking related to proof, generalization, alternative answers, and problem-solving. This online learning involved 30 prospective mathematics teachers through video conferences. An exploratory case study was conducted on 9 mathematics teacher candidates with the highest exam scores. Data were collected from the results of 4 mathematical critical thinking questions. The data were analyzed and described based on a predetermined framework. The results show various epistemological obstacles in critical thinking, namely difficulty in proving the relationship between two concepts, generalizing the relationship, finding multiple alternative solutions, and solving problems. The epistemological obstacles found can be the focus of lecturers in creating more structured online learning. Online learning needs to be well-planned in terms of the use of learning resources, learning media, and integration with technology. Learning should pay more attention to understanding the relationship between concepts, the flexibility of concepts and procedures, as well as the habit of drawing in geometry learning.