To　improve　the　deficiency　of　the　wave　input　method　(WIM)　in　expressing　complex　incident　site　waves,　in　this　paper,　a　random　non-uniform　wave　input　method　(RNUWIM)　is　derived　from　the　use　of　the　random　incident　waves　and　the　visco-elastic　boundary　condition.　The　random　incident　waves　are　generated　and　adjusted　by　the　comparison　of　the　horizontal　ground　motion＇s　response　spectrum　and　the　target　spectrum,　so　that　they　are　representative　of　the　actual　wavefield　in　project　sites.　Furthermore,　the　RNUWIM　is　implemented　and　verified　by　the　finite　element　method.　The　result　shows　that　the　RNUWIM　inherits　the　advantages　of　the　WIM　in　simulating　the　wave　propagation　effect　and　the　radiation　damping　effect.　In　the　new　method,　the　spatial　variation　of　ground　motions　such　as　time　delays,　peak　variation,　and　time-history　shape　differences　can　be　simulated　synthetically.　The　errors　of　RNUWIM　in　ground　acceleration,　velocity,　and　displacement　at　the　reference　point　are　respectively　3.23%,　0.66%,　and　0.07%　in　one　case,　which　proves　the　efficiency　of　the　RNUWIM　in　seismic　response　analyses.　©　2023　Elsevier　Ltd