The purpose of this study is to identify primary school students' thinking processes within the mathematical modeling process and the challenges they encounter, if any. This is a basic qualitative research study conducted in a primary school in the city of Kütahya in the academic year of 2015-2016. The study group of the research was composed of 22 students at 4th-grade who were selected with criterion sampling which is a purposive sampling method. The study data were collected with the clinical interview method and reported using the content analysis. It was consequently found that the students constituted two groups as those who provided a realistic solution and those who could not. There were more students who could not provide a realistic solution. Those who could not provide a realistic solution tried to construct the mental representation of real situation through literal comprehension, which became insufficient in revealing the hidden situations involved in the problem text. Not noticing the hidden actions in the text led them to form a mathematical equation without structuring the problem and thus their solutions were unrealistic. Those who could provide realistic solutions, on the other hand, decided their operations within the context of the characters, time, place and relation between the events in the problem, which enabled the mental representation of the problem text to be critical reading and inferential comprehension focused as well as literal comprehension focused and thus allowed the students to reveal the hidden situations in the text. Accordingly, students posed new problems by gathering the required extra information according to these hidden situations and went for the real model. Thus, analyzing the problem situation in various contexts, students solved according to multiple conditions. It was also seen that students with realistic solutions utilized the validation process to determine the consistencies and inconsistencies of their solutions in real life context while those with unrealistic solutions utilized it to check their operations.