A slicing machine includes a tapered slicing gate for use in cutting products such as potatoes or the like into a plurality of slices each having a tapered thickness. The slicing machine generally corresponds to U.S. Pat. No. 3,521,688 and includes a rotary impeller for carrying the products by centrifugal force against an interior surface of a nonrotating cylindrical outer impeller housing, a portion of which defines an adjustable slicing gate forming a cutting slot of controlled thickness relative to a stationary slicing knife for cutting the products into the plurality of slices. A tapered ramp is formed or mounted at a downstream end of the slicing gate so that the cutting slot and the resultant slices have a tapered configuration. The tapered slices may be cut further into elongated strips, such as French fry potato strips, having a tapered lengthwise thickness.