In　this　work,　a　recursion　reverberation-ray　matrix　method　(RRRM)　is　presented　to　formulate　an　exact　and　unified　solution　for　the　non-stationary　responses　analysis　of　the　sandwich　panels　with　corrugated　cores　(SPCC)　subjected　to　the　moving　random　loads.　The　governing　equations　for　the　basic　units　are　obtained　by　employing　the　simple　first-order　shear　deformation　theory　(S-FSDT)　and　Hamilton＇s　principle.　Then,　based　on　the　traditional　reverberation　ray　matrix　method　(MRRM),　the　RRRM　is　established　by　incorporating　a　bidirectional　recursion　technique　to　effectively　calculate　the　exact　solutions　of　the　whole　model.　Thereinto,　the　kinematic　relation　matrix　between　the　cell　units　can　be　constructed　to　facilitate　the　coupling　of　various　desired　numbers　of　elements　by　employing　the　virtual　coupling　spring.　In　addition,　a　unified　loading　mechanism　for　multi-scenario　loads　is　proposed　by　integrating　the　pseudo-excitation　method　(PEM)　with　the　load　stage　division　technique.　The　applicability　and　accuracy　of　the　current　method　to　non-stationary　response　behaviors　of　the　SPCC　are　clarified　by　carrying　out　sufficient　comparative　studies　between　the　calculated　results　with　reference　solutions　from　FEM　and　Monte　Carlo　simulation　method.　Furthermore,　several　meaningful　conclusions　are　drawn　regarding　the　effects　of　structural　and　load　parameters　on　the　vibration　characteristic,　non-stationary　displacement　response,　power　spectrum　density　(PSD),　and　time-varying　root　mean　square　(RMS).