Abstract: An apparatus forms boxes with curved corners from a die-cut sheet. A forming matrix delimits a forming cavity by guides counterposed in pairs along two orthogonal axes. The guides define a die-cut sheet support plane. A forming head inserts inside the cavity to push the die-cut sheet to form a box. Vacuum gripping devices are arranged outside the cavity in opposite positions along the second axis and each grip from underneath the die-cut sheet to hold it on the support. Pusher devices are arranged outside and near one of the corners of the cavity. Each pusher device raises one side flap of the die-cut sheet from the support plane. An electronic control unit operates the main gripping devices, pusher devices and forming head according to the following sequence: actuating the gripping devices; actuating the pushers; deactivating the gripping devices; and inserting the forming head in the forming cavity.