A machine (100) for making filter bags (1) of tetrahedral shape for infusion products (P) comprises a production line (L) defined by a series of operating stations (50, 9, 10, 14, 11, 12, 13) where filter bags (1) made from a continuous flattened tube (2) of filter paper are formed, filled with respective doses of infusion product (P) and subjected to successive cuts and closing seals (SL, ST, SC). The production line (L) extends in a direction parallel to the direction (A) and comprises, in succession, a first sealing station (50) for making the first longitudinal seal (SL) to form the tube (2) so that it extends in the horizontal direction (A); a second tube (2) sealing station (9) for making a succession of transversal seals (ST) on the tube (2) transversally to the horizontal direction (A); a cutting station (10) for cutting the tube (2) at the transversal seals (ST) so as to create a succession of filter bags (1) in the process of being formed, each having a sealed bottom end and an unsealed end (7); a station (11) for opening the unsealed end (7) of each filter bag (1); a station (12) for dosing the infusion product (P), where a dose of the product (P) is inserted into the filter bag (1) through the unsealed opened end (7); and a third sealing station (13) for making a seal (SC) that closes the end (7) of each filter bag (1) that is still open; the closing seal (SC) extending in a direction transversal to the aforementioned longitudinal seal (SL) and to the aforementioned transversal seal (ST).