Abstract: The impact problems of a rod on a Timoshenko beam and a Timoshenko beam on another Timoshenko beam were analyzed by means of the indirect mode superposition method(IMSM). A rod on a beam and a beam on another beam are both typical built-up structures. The displacement compatible equations of the two problems were established by IMSM on the basis of the individually obtainedmode functions and frequencies of impactors and targets, and solved by numerical integration step by step. The numerical analysis by making use of dimensionless variables show the propagation of the longitudinal waves along rod, and the longitudinal and transverse waves along beam, and the mutual transition and reflection between the longitudinal waves and the transverse waves in the impact built-up structures in detail.