A meat cutting band machine for slice cutting soft meats. The machine (10) comprises a base (11) and a vertical band blade support frame (15) secured to the base (11). A pair of band blade wheels (16, 16') are rotatably supported in a spaced apart manner on the band blade support frame (15). A flat band blade (17) is drivingly supported about the wheels (16, 16'). A drive (18 to 22) is provided to rotate the wheels (16, 16') and the blade (17). An opening (24) is provided in the band blade support frame (15) to expose a meat cutting area (25) along a straight path of the band blade (17). A stationary table (14) is secured below the meat cutting area (25). A horizontally displaceable meat support table (26) is displaceable on an axis parallel to the plane of the flat band blade (17) to displace an end portion of a piece of meat placed on a support surface thereof against a cutting edge of the band blade. The horizontally displaceable meat support table (26) has its support surface inclined rearwardly downward with the band blade (17) extending at substantially a right angle with respect to the support surface of the displaceable meat support table (26).