Modelling is an inherent process for the construction and use of science concepts that mobilize diverse specific competences. The aims of this work are to put forward a means of evaluating modelling competences that is relevant for physics teaching and science education research and to identify the potentials and constraints in the development of modelling competences. A written test, which embraces a wide range of modelling aspects in mechanics domain, was drawn up and validated, and a theoretically based evaluation methodology was specified. In the validation process, the test was given to 75 subjects distributed across seven levels of physics education. The answers were analysed and later cluster analysis was carried out in order to identify categories of answers among the diverse answers. The results indicate that the test identified and delimitated modelling competences. Some results are in agreement with those obtained through other research into this issue and other results better elucidate certain aspects of modelling. The way in which evaluation methodology can be used in other areas of physics is discussed, such as in research and in teaching. Also discussed is how the constraints and potentials identified in the development of modelling competences can be taken into account in teaching and learning sciences. (Contains 14 tables and 3 figures.)