Asanimportantmodelinquantumsemiconductordevices,theSchrodinger-Poissonequationshavegeneratedwidespreadinterestsinbothanalysisandnumericalsimulationsinrecentyears.Inthispaper,wepresentGaussianbeammethodsforthenumericalsimulationoftheone-dimensionalSchrodinger-Poissonequations.TheGaussianbeammethodsforhighfrequencywavesoutperformthegeometricalopticsmethodinthattheformerareaccurateevenaroundcaustics.ThepurposesofthepaperarefirsttodeveloptheGaussianbeammethods,basedonourpreviousmethodsforthelinearSchrodingerequation,fortheSchrodinger-Poissonequations,andthenchecktheirvalidityforthisweakly-nonlinearsystem.