Abstract: Transient acoustic scattering contains rich information about objects. This paper studied the divergence in computation of the transient acoustic scattering by use of the time domain integral equation method. A calculation technique provided stable results for a long time calculation is presented. We extended the time domain integral equation method to the impedance object, and computed the transient acoustic backscattering of a hard and an impedance cylinder with a spheroidal end cap. The results show that the transient echoes have features of the highlight.