In this paper, the effect of blade root damping on the resonant amplitude of blade with simple dovetail root and the effect of root flexibility on the blade vibration are analysed by means of the FEM. The slip between the root and disc is treated as a sort of dynamic contact problem and a Computational method is offered. The root is discretized by plane-strain elements and the blade by the plate element. In the spirit of substructure synthesis, a method for reducing the degree of freedom is presented and a satisfactory result is obtained.