This study was conducted to examine peer tutoring models in collaborative learning of mathematical problem solving (MPS) in flipped classrooms and their effect on group achievement. Quantitative data collected include 32 videos of eight groups of students in four MPS periods that were designed based on a simplified version of Polya's four-stage model, and their worksheets completed in each period. The video data were coded based on a framework with low-level and high-level cognitive behaviors as well as management behaviors and were analyzed using lag sequence analysis from which three types of peer tutoring models were determined: organization-oriented, cognitive-supported, and cognitive-guided. ANOVA analysis showed that the groups with cognitive-guided tutors performed significantly better than the groups guided by cognitive-supported and organization-oriented tutors, between which the performance difference did not reach a significant level. The results of this study suggest that training provided to peer tutors should focus more on how to stimulate high-level cognitive thinking skills than on organization skills.