The aim of this research is to determine the current models for geometric series produced by the middle school teacher candidates and classify these models. A case study of the qualitative research method was adopted in this research. This research was conducted with final year pre-service mathematics teachers studying elementary mathematics (n=41). This research applied at a state university in the large-scaled city of Eastern Anatolia Region of Turkey was carried out in the fall semester of 2013-2014 academic years. Data collection tool of the research is the paradox named “Tortoise Paradox” in the literature posed by the Greek Mathematician Zeno. The answers obtained from the detailed modeling examples of teacher candidates were examined with the descriptive analysis. According to the results of the research, it is seemed that teacher candidates have difficulty in drawing appropriate mathematical model for tortoise paradox. Also, it has been found that these difficulties have increased even more. Teacher candidates showed inadequate approach on the steps named “interpretation the results in a real situation” and “solution verification” among the modeling steps. Also, teacher candidates have used the most algebraic and visual models in the modeling process. But, it has been determined that very few of the mathematical models produced by teacher candidates are compatible with the logic of the problem.