The　present　work　primarily　aims　to　provide　a　general　stochastic　vibration　system　for　the　stepped　composite　cylindrical　shells　with　drop-off　ply　subjected　to　moving　loads.　By　performing　the　first　-order　shear　deformation　shell　theory　(FSDST)　and　Hamilton＇s　principle,　the　theoretical　model　is　established　and　the　stationary/nonstationary　stochastic　responses　are　solved　by　integrating　the　pseudo　excitation　method　(PEM)　into　the　method　of　reverberation　-ray　matrix　(MRRM).　Meanwhile,　the　unsymmetrical　drop-off　ply　configuration　is　realized　by　considering　a　balanced　relationship　through　the　artificial　virtual　springs　at　the　coupling　point.　The　novelty　lies　in　the　sequential　action　of　moving　random　load　on　non　-uniform　stepped　cylindrical　shells　in　the　form　of　concentrated　or　distributed,　and　a　unified　full　-domain　response　formulation　containing　the　nonhomogeneous　excitation　equation　is　provided.　The　comparison　of　the　stochastic　vibration　response　curves　and　deformation　diagrams　with　the　finite　element　simulation　demonstrates　that　the　current　method　is　effective　for　various　stochastic　dynamic　problems.　On　this　basis,　the　differences　between　the　unsymmetrical/symmetrical　drop-off　ply　configurations　under　moving　random　loads　are　first　visually　discussed,　and　the　effects　of　the　load　and　geometric　parameters　on　the　power　spectrum　density　(PSD),　frequency　response　bandwidth　and　time　-varying　root　mean　square　(RMS)　are　further　revealed.