Abstract: The dynamic substructure method was proposed to accountfor propagation of elastic-plastic waves in flexible components induced byimpact. A dynamic model using the substructure technique was established andits governing equations in modal coordinates were derived from the finiteelement theory and the substructure synthesis method. The existence of thenormal modes in the indicated waves and the convergence of the truncation ofthe normal modes were proved. Numerical cases are illustrated forlongitudinal and transverse impact of flexible bars. The simulation results,the comparisons with their analytical solutions, and calculations of thethree-dimensional dynamic finite element method, show that the presentmethod is convergent and valid.