For　the　first　time,　this　work　presents　a　comprehensive　analysis　of　the　forced　and　post-forced　vibration　responses　for　the　multi-stepped　composite　cylindrical　shell　(MSCCS)　subjected　to　moving　excitation　with　the　general　distribution.　Based　on　the　method　of　reverberation-ray　matrix　(MRRM)　of　the　general　connection　conditions,　the　investigated　structural　system　composed　of　several　cylindrical　shells　having　different　lengths　and　thicknesses　is　modeled　analytically　by　the　inhomogeneous　dynamic　equations　with　introduced　the　continuous　acting　mechanism　of　the　moving　excitations　precisely.　In　order　to　address　the　discontinuity　problem　of　the　moving　excitation　at　the　multi-stepped　connections,　a　coupling　technique　involving　the　recombination　of　wave　numbers　and　a　matrix　excitation　coordinate　transfer　scheme　is　adopted.　This　approach　allows　for　a　flexible　span　of　axial　loading　and　arbitrary　circumferential　distribution.　The　verification　results　exhibit　excellent　accuracy　for　dealing　with　the　transient　responses　under　various　moving　excitations　of　the　MSCCS.　The　novel　parameters　examples　reveal　that　the　post-forced　vibration　phenomenon　can　be　eliminated　within　a　certain　parametric　range　instead　of　changing　the　load　velocity.　Furthermore,　the　thickness　ratio,　axial　loading　span　and　circumferential　distribution　also　play　an　important　role　in　the　dynamic　responses　under　moving　excitations.　©　2024　Elsevier　Ltd