A new method for predicting the position of the galling generation in square cup drawing is proposed on the basis of fact that galling at a drawn cup occurs at the position of maximum temperature and at the moment the position is sliding out of the die. Blank of three shapes, square, octagon, and triacontadigon, are used to change the galling position on the drawn cup. FEM simulation shows that galling on the drawn cup occurs at the top of the boundary between the drawn area and the bent area for the square blank and at the top of the middle of the drawn zone for an octagonal or triacontadigonal blank. Demonstrations using a high-tensile-strength steel sheet under a lubricated condition show that galling on the drawn cup does occur as predicted by FEM simulation. Galling on the die surface remains at the path end of the galling position of the blank material. It is also found that the sliding distance after the galling position of the blank attains the maximum temperature markedly, greatly affects the galling generation: the longer the sliding distance is, the easier the galling generation becomes.