The machine comprises a rotating drum (29) endowed with a circumferential succession of squeezing members (38) arranged along generators of the drum. The squeezing members consist of pairs of pincers (38) urged in relative translation between an open position and a closed position for the formation of sausages (23) connected by narrow appendices (59). There is provided a circumferential succession of pairs of twisting rollers (55) interpolated with the squeezing members (38) and operated to engage the sheaths (34) of the sausages (23) already formed so as to cause alternatively opposed torsions of the sheaths themselves for their corresponding twisting at said appendices (59). There can be provided shearing members (40) associated with the squeezing pincers (38) and operated, with pincers closed, to perform the shear of the appendices (59) for the separation of the sausages (23).