A machine (1) for cutting a strand shaped food material, in particular meat or cheese into slices, comprising: a feed portion (2); a cutting device (3); and a conveying portion (4), wherein a food material strand (63) is moveable in feed direction (38) from the feed portion (2) through a feed device (37) towards the cutting device (3) including a rocker (6) pivoting about a first rotation axis (7) fixated at a housing, wherein a circular blade (10) is supported at the rocker and configured to be driven in rotation about a second rotation axis (9) and configured to cut successive slices from a front face of the food material strand (63), wherein the slices are transferable into the conveying portion (4) after being cut off from the food material strand (63), wherein the feed device (38) is substantially horizontal, and wherein a circular path (K) on which the second rotation axis (9) orbits is arranged completely outside of a maximum cross section.