The extraction system of a cyclotron guides an ion beam from a spiral acceleration orbit, through an extraction trajectory, into a high energy transport line. The two methods commonly used to direct an ion into the extraction path are deflection, by the electric field of an electrostatic deflector, and ion stripping, by a thin carbon foil. Compared to the electrostatic deflector system, the stripping extraction provides a fast and easy change of the extracted ion energy and is easier to manufacture operate, and maintain. However, the extraction trajectory and dynamics of an ion beam after stripping are highly dependant on the ion energy and specific charge. Thus, when a multipurpose machine such as the VINCY Cyclotron is concerned, it is far from easy to deliver a variety of ion beams into the same high energy transport line and at the same time preserve a reasonable compactness of the extraction system. The front side stripping extraction system of the VINCY Cyclotron provides high (~70 MeV) and mid (~30 MeV) energy protons, as well as a number of heavy ions in broad energy ranges. The back side stripping extraction system extracts low energy protons (~18 MeV) and enables their simultaneous use with high energy protons at the front side of the machine.