An important mechanism reducing the lifetime of the deepdrawing tools is material transfer from the workpiece to the tool, resulting in the buildup of lumps on the tool surface. In this study, a lump growth model, based on transfer mechanisms observed in experiments, is developed. The development of the summit height distribution of the tool surface is calculated from the growth behavior of the individual lumps. Important parameters influencing material transfer are determined from the calculated summit height distributions. It follows that lump growth can be decreased and, under certain conditions prevented, by a higher (surface) hardness of the workpiece, a lower roughness of the tool surface, a lower nominal contact pressure, and a lower shear strength of the interface. These results are in general agreement with results obtained from experiments. Experimental results are presented in an accompanying paper (de Rooij and Schipper, 2000).