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In this paper, the production of stainless steel hemi-toroidal parts has been investigated using three different processes: the conventional stamping, the standard sheet hydroforming and the hydroforming adopting a movable die (MD) which can have a vertical stroke and whose shape completes the female die cavity. Tests adopting the MD were performed at Aalborg University using a specific experimental equipment; numerical simulations were performed using ABAQUS\Explicit and were aimed at investigating the effect of the friction condition of the MD tool on the blank deformation. The friction coefficient was varied on both the whole surface of the MD tool and locally (in the region of the MD corner radius). The role of the MD in the hydrofonning process was thus studied by comparing results in terms of thickness and strain distributions on the final part obtained adopting the same geometry of tools, but different forming techniques. Simulations put in evidence that a moderate increase of the friction can be successfully used for reducing thinning if the MD is adopted; in addition, the friction in the region of the MD corner radius shows to play a key role in forming sound parts.