Abstract: In flexible multi-body dynamics with contact/impact, multi-variable method (MVM) which is based on appended contact constraint model is proposed. With this method, two types of variables are used to describe the flexible body deformation: small superposed deformation is depicted with finite element nodal coordinates in contact region and modal coordinates in non-contact region respectively, thus this method takes account of both accuracy and efficiency. This method is extended to three-dimensional spatial contact issue which is more complicated than the planar one, and the numerical simulation of a longitudinal impact between two rods agrees well with the experiment result. To solve the variable selection problem, the influences on result accuracy of node position, modal orders and material parameter are studied. Based on this, the optimal multi-variable selection is realized which reduces the DOFs to the maximum extent and also achieves accuracy in the same time.