This study aims to investigate students' problem solving approaches by examining students' use of mathematical models. In this research, since many students think that the concepts of relativity are unfamiliar, abstract and difficult, it was focused on relativistic kinematics-the relativistic Doppler Effect. Sophomores from two cohorts of physics (n=60) and physics teaching (n=32) enrolled in a modern physics course at a university participated in the study. Participants were asked to provide extended written responses to the Doppler Effect problems with a test. Afterwards six students were purposefully selected for semi-structured interviews. Students' use of mathematical models revealed that students had difficulty in discriminating between fundamental concepts such as frequency and wavelength, source and observer, red-shift and blue-shift, and they consequently used these concepts interchangeably. In addition, because of students' the lack of ability of representing the problem in different forms according to a given physical context, they also had difficulty in determining the appropriate model. In conclusion, students used both physically and mathematically meaningless models and their problem solving approaches varied due to the use of mathematical models.