Mathematical model and modeling are one of the topics that have been intensively discussed in recent years. The purpose of this study is to examine prospective elementary mathematics teachers' thought processes on a model eliciting activity and reveal difficulties or blockages in the processes. The study includes forty-five seniors taking the course of Modeling in Teaching Mathematics in an elementary education program at a university. Three prospective teachers were selected among them and then interviewed in a focus group. The transcription of conversation of the group was examined and qualitatively analyzed. Findings indicated that prospective teachers were able to successfully work with modeling eliciting activity and improve their mathematical understandings. They also showed some difficulties while working on the modeling activity.