The stick-slip vibration is introduced as a new mechanism to explain the large amplitude torsional oscillation of the drill strings in oil and gas well drillings. A record of field data is identified and simulated according to the new mechanism. The analytical results derived from the numerical simulation agree with the field data with 95.6 percent accuracy. The physical phenomenon of the stick-slip vibration of drill string is explained by initiating a phase trace in the phase plane. The beating phenomenon in drilling is interpreted in terms of stick-slip vibration. The effects of viscous damping, rotary speed and natural frequency on the stick-slip vibration are discussed.