The motion of a cylindrical piston falling in a liquid filled vertical cylinder is analyzed. It is found that concentric motion is impossible and that flow induced vibration is always associated with such piston-cylinder systems. If the clearance over radius ratio is larger than a certain critical value, βcr, severe wobble and piston-cylinder contact occurs. For clearance over radius ratio less than βcr stable periodical oscillation with a constant amplitude takes place and the piston never contacts the cylinder wall. Reasonable agreement is achieved between the theoretical results and previous experimental observation.