Authors have been working in particle accelerator wake field analysis by using the Time Domain Boundary Element Method (TDBEM). A stable TDBEM scheme was presented and good agreements with conventional wake field analysis of the FDTD method were obtained. On the other hand, the TDBEM scheme still contains difficulty of initial value setting on interior region problems for infinitely long accelerator beam pipe. To avoid this initial value setting, we adopted a numerical model of beam pipes with finite length and wall thickness on open scattering problems. But the use of such finite beam pipe models causes another problem of unwanted scattering fields at the beam pipe edge, and leads to the involvement of interior resonant solutions. This paper presents a modified TDBEM scheme, Scattered-field Time Domain Boundary Element Method (S-TDBEM) to treat the infinitely long beam pipe on interior region problems. It is shown that the S-TDBEM is able to avoid the excitation of the edge scattering fields and the involvement of numerical instabilities caused by interior resonance, which occur in the conventional TDBEM.