Abstract: During drilling operation,the jack-up drilling rig is similar to a fixed offshore platform and the upper part of legs stretched above the hull may vibrate as a cantilever beam.Based on the equivalent beam theory in which the effect of shear deformation is considered,formulas are derived to analyze the eigen periods of rigs and their cantilever legs.A spatial truss model has been suggested to calculate the stiffness of legs of the truss type; the periods computed simply by hand agree well with those computed with traditional spatial frame model by computer.In 1978,the cantilever parts of the legs of "Bohai 4",a jack-up drilling rig with three legs of triangular section,suffered serious wind-induced oscillations when operating at water depth of 25 meters.Vibration measurements show that these oscillations are predominantly twist motions.The shedding frequency of vortex approaches the fundamental torsional frequency of cantilever legs at a wind speed of 14～15m/sec.It is also shown,both theoretically and experimentally,that the fundamental period of operation of the drilling rig at water depth deeper than 30 meters will be longer than 3 seconds,so the dynamic response of rigs to wave-induced excitationcan be significant even if resonance does not occur.