The purpose of this case study is to examine the design process of the Model Eliciting Activity (MEA) named Obesity Problem designed by four mathematics teachers and the MEA itself in the framework of MEA designing principles. The data are the MEA and the transcriptions of the records videotaped in the design process. The records were analyzed using content analysis and the MEA was analyzed using document analysis. The MEA was completely appropriate for the reality, model construction, construct documentation and model generalization principles, and partially appropriate for the self evaluation principle. The effective prototype principle could not be identified. The teachers starting the design process from real life situations constructed a generalizable and appropriate model for the students.