Abstract: Base on the idea of alternating frequency/time(AFT) domain,an approach to predict the nonlinear response of a shrouded blade system was developed using free mode shapes.Some sources of error in the process of previous AFT were eliminated and the instantaneous variety of contact stiffness was taken into account,improving evidently the correctness and efficiency.Comparison of the calculated and experimental results proves that this method meet the engineering need of blade damping design fully.Furthermore,influences of the number of free mode shapes on the calculated results are studied.It is found that in the neighborhood of the fully slip region,few number of free mode shapes are required in order to obtain the accurate resonant response of a shrouded blade system;however,it need much more number of free mode shapes to obtain the accurate response in the neighborhood of the fully stuck region.