This paper presents an analytical model at the cylindrical coordinate system for the power consuming of the viscous force caused by centripetal force of the drill string while rotating without weight on bit (WOB). The drilling mud in this model is assumed to be Newton fluid. Therefore, this model has a good accordance with the reality by synthetically considering the rotate angular velocity, the structure parameters of the drill string and the well, the viscous coefficient of drilling mud and etc. That is, the centripetal forces of the drill string and the shearing strength caused by the fluid are considered in the model, which makes it have a better utility than those existing.