Abstract: Multi-variable method is proposed to dealwith flexible multi-body systems with contact/impact. With this method, thefloating reference frame technique is combined with the nonlinear finiteelement technique to raise the solving efficiency of the whole system andthe computation accuracy in the local contact/impact region. The motion ofthe non-contact/impact region is described with the floating reference frametechnique and the modal reduction approach is used to raise thesolving efficiency. The nonlinear finite element technique is employed fordescribing the nonlinear and plastic deformation in the local contact/impactregion. Some numerical examples are presented with the proposed method. Inaddition, experimental investigations with a Laser-Doppler vibrometer arepresented. The numerical results agree well with the experimental ones.