The deformation of the press and the forming tools during a deep drawing process is small. However, it has a significant influence on the formed product, since the draw-in is affected significantly by this deformation. This effect is demonstrated for the cross-die forming process. The process was simulated using the commercial code ABAQUS, comparing different models for the forming tools and blank. The simulated process behaves quite differently when rigid or deformable tools are applied. In the latter case, so-called tool-spacers absorb a significant part of the blankholder load, resulting in a stronger draw-in of the blank. In all cases, the results depended heavily on the blank element type and on numerical settings for the contact algorithm. These should be treated with great care when accurate results are required.