The purpose of this study is to identify the difficulties that preservice elementary mathematics teachers have experienced in solving the experimental and theoretical modeling problems and to show how the effect of computer usage is in eliminating these difficulties. The study sample consisted of 20 preservice teachers in their last year at the elementary mathematics education program. Each of the preservice teachers has experience with mathematical modeling and using GeoGebra software. The participants worked on six mathematical modeling problems, three experimental and three theoretical problems, in groups of four. The data were collected from the videos recorded during their work, the focus group discussions, the screencasts of the groups on the computers and the observation notes of the researcher. Qualitative analysis techniques were used in the analysis of the data. The determined codes are classified under the steps of the mathematical modeling process. The results show that preservice teachers encountered a variety of difficulties in each phase of the modeling process. They had more difficulty with theoretical modeling problems than with experimental modeling problems and the use of computers significantly contributed to the elimination of the difficulties. The fact that preservice teachers had a lot of confidence in the results obtained through the use of computer in modeling and verifying this model, has emerged as a negative effect of computer technology.