The main contribution of this paper to current philosophical and sociological studies on modeling is to analyze modeling as an object-oriented interdisciplinary activity and thus to bring new insights into the wide, heterogeneous discourse on tools, forms and organization of interdisciplinary research. A detailed analysis of interdisciplinarity in the making of models is presented, focusing on long-standing interdisciplinary collaboration between specialists in infectious diseases, mathematicians and computer scientists. The analysis introduces a novel way of studying the elements of the models as carriers of interdisciplinarity. These elements, being functionally interdependent building blocks, evolve during the modeling work and carry the disciplinary tensions in the process. This shows how the long and challenging process of defining and reformulating the object of research is crucial for understanding the dynamics of interdisciplinarity in the making.