The purpose of the study is to reveal the elementary mathematics student teachers' difficulties encountered in the solution of a modelling problem, the strategies to overcome those difficulties and whether the strategies worked or not. Nineteen student teachers solved the modelling problem in their four or five-person groups, and the video records of their solution processes and their solution papers were examined. They had difficulties in simplifying, mathematizing, interpreting and validating and developed different overcoming strategies such as using the figure in the problem, real life experiences, utilizing a real object, answering the researcher, group discussion, sketching, reading the task back, considering calculation simplicity and some others peculiar to the problem. When they could overcome the strategies in simplifying and mathematizing, they could not be successful in tackling with those in interpreting and validating.