The disclosure is directed to a thermoforming packaging machine (1) for producing upright standing packagings (21) with an undercut (26) formed into the packaging. The machine comprises a forming station (2) with a lower forming tool (30) and/or a sealing station (3) with a lower sealing tool (40). The disclosure is characterized by the lower forming tool (30) and/or the lower sealing tool (40) comprising a movable forming wall section (32) or a movable sealing seam support section (41a), respectively, in the area of the undercut (26). The disclosure is also related to a corresponding method for producing packagings (21).