Machine for cutting food products into wavy sticks (62; 63), comprising: - an annular-shaped cutting head comprising a plurality of cutting stations, each cutting station comprising at least a wave-shaped blade that extends vertically and a plurality of blades that extend horizontally and are superimposed on and spaced vertically from one another, said wave-shaped blade being formed with wave peaks and wave troughs, each of said cutting stations comprising a support device (24; 124) of said wave-shaped blade that extends vertically, and a support device of said plurality of blades that extend horizontally, which are detachably mounted in said support device; - a rotatable drum coaxially disposed within said cutting head, provided with blades placed along the outer edge of said drum; - motor means of said drum, operatively adapted to rotate said drum about its vertical axis; characterized in that: - said wave-shaped blade that extends vertically has a cutting edge projecting from said support (24; 124), said support devices (24, 124; 34) of said wave-shaped blade and of said plurality of blades that extend horizontally are spaced radially from each other; said blades that extend horizontally are formed with a cutting edge oriented towards the inside of said cutting head and forming an angle (δ) with respect to said cutting edge of said wave-shaped blade, said blades that extend horizontally being aligned with said wave peaks of said wave-shaped blade; whereby the food product to be cut, which is fed towards the cutting stations, first encounters said wave-shaped blade then said plurality of superimposed blades that extend horizontally. - an annular-shaped cutting head comprising a plurality of cutting stations, each cutting station comprising at least a wave-shaped blade that extends vertically and a plurality of blades that extend horizontally and are superimposed on and spaced vertically from one another, said wave-shaped blade being formed with wave peaks and wave troughs, each of said cutting stations comprising a support device (24; 124) of said wave-shaped blade that extends vertically, and a support device of said plurality of blades that extend horizontally, which are detachably mounted in said support device; - a rotatable drum coaxially disposed within said cutting head, provided with blades placed along the outer edge of said drum; - motor means of said drum, operatively adapted to rotate said drum about its vertical axis; - said wave-shaped blade that extends vertically has a cutting edge projecting from said support (24; 124), said support devices (24, 124; 34) of said wave-shaped blade and of said plurality of blades that extend horizontally are spaced radially from each other; said blades that extend horizontally are formed with a cutting edge oriented towards the inside of said cutting head and forming an angle (δ) with respect to said cutting edge of said wave-shaped blade, said blades that extend horizontally being aligned with said wave peaks of said wave-shaped blade; whereby the food product to be cut, which is fed towards the cutting stations, first encounters said wave-shaped blade then said plurality of superimposed blades that extend horizontally.