The term mathematical modelling covers a wide range of activities. These are not only purely mathematical skills but also skills referring toa framework of modelled situation. For this reason, acquiring the skills of mathematical modelling brings a number of teaching benefits. This ability is connected with necessary competencies related to mathematical modelling. Mathematics students – prospect teachers of mathematics, should acquire these skills before they start teaching mathematical modelling. Is it really so? The paper presents the results of the research on competencies in students’mathematical modelling abilities. We show in what way prospect teachers are able to learn the elements of mathematical modelling on their own. Ther esearch proves the need to review the issue of mathematical modelling in the training of mathematics teachers.