Abstract: This paper presents a further discussion on Duhamel integral, which is a classical method in solving the dynamic response of a linear system subject to an arbitrary excitation. Based on the basic idea of resolving an arbitrary excitation into infinite number of impulsive excitations, the implementation procedure of the pulse excitations for Duhamel integral is thoroughly discussed from both the way of accumulation in series and the way of superposition in parallel. A new mathematical proof by approach of calculus is provided for verification of Duhamel integral.