Abstract Based on the residual dynamic flexibility, a new definition of the inertia relief attachment mode is proposed. The approximated representations of residual mass and residual stiffness are deduced by partly ignoring the dynamic effects of the truncated modes. The free interface component mode synthesis method is used to set up the dynamic model of the full structure by coupling experimental model of component A and finite element model of component B. Finally, numerical examples have demonstrated the validity and efficiency of proposed method. Furthermore, the results indicate that the influence of the residual mass and residual stiffness on the accuracy of final results can be neglected.