This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future classroom practices. The participants of this study were six prospective teachers selected among the nineteen who enrolled in the course. Data was collected through five modeling tasks. The results showed that the prospective teachers went through five main stages during the modeling process: understanding the task, devising a solution plan, working out the plan, interpreting and verifying the model, and presenting the model. The nature of prospective teachers' modeling processes was rather result-oriented, consisting of a single cycle as they did not seek an improved solution by revising and refining their models.