This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling course, offered for the first time as an elective course in a secondary mathematics teacher training department in a public university in Turkey. The data were obtained from the modelling problems prepared by the pre-service mathematics teachers in the last 3 weeks of the Mathematical Modelling course, the video recordings of these problems' presentations and the pre-service teachers' responses to the questions they were asked about their presentations. When analyzing the participants' approaches to construct and solve mathematical modelling problems, the main focus of attention included the appropriateness of the problems for modelling and of the solutions to the modelling process, as well as the approaches displayed in these stages. The study's results demonstrated that the pre-service teachers considered various criteria when constructing modelling problems such as relevance to life, the possibility of being solved by mathematical knowledge and attracting attention and were found to be successful in understanding and simplifying the modelling process, however, they had difficulties in the interpreting and validating steps.