Abstract: An automatic machine is provided for slicing non-rigid products, such as foodstuffs or meats. The machine includes a carriage with a plate supporting the product to be sliced. This carriage is mobile in relation to the cutting assembly which permits the product to be sliced. The machine further including a device for removing the cut slices. A control circuit is provided for receiving information from a detector. An input terminal controls the angle between the plate of the carriage thereby making the angle between the plate and the carriage adjustable.