Galling is a recurring phenomenon in deep drawing processes which requires frequent maintenance of tools to improve the product surface quality. Adhesive transfer of softer material on the hard tool surface results in sharp features which causes surface roughening of the tools and deterioration of deep drawn products. In this article, an adhesive wear model based on a deterministic approach is developed to predict the galling behavior in a deep drawing process. The model uses the surface topography, material properties and contact conditions to predict the surface roughening of tool surfaces under perfectly plastic conditions. The adhesive transfer of material is considered by the growth of the asperities based on its geometry for the increase in height and radial direction by preserving the original shape and volume consistency. The results of the multi-asperity models show the growth of the transfer layer and its effects due to load, sliding cycle, sliding distance, and affinity of the materials. The results show the influence of the above-said parameters and its applicability for deep drawing process conditions. The simulated results show an 85% level of confidence in comparison with the experiments from literature for the prediction of the surface evolution due to the galling mechanism.