Meat slicing machine, comprising a belt blade (5) conceived to follow a straight cutting line (50) for the meat to be sliced, characterised in that it comprises a support surface (9) parallel to the cutting line (50) and set at a distance from the line at right angles to the support surface (9) itself; a container (11) for the meat to be sliced, having an exit opening (12) facing the said support surface (9) on the side of the cutting line (50); Pushing devices (13) associated with said container (11), conceived to push the meat down towards said exit opening (12); and a moving mechanism (19, 22) conceived to translate the container (11) in a parallel manner to the support surface (9) with a backward and forward motion from one side of the cutting line (50) to the other.