Whenthehigh-pressuregasisexhaustedtothevacuumchamberfromthenozzle,theunderexpandedsupersonicjetcontainedwiththeMachdiskisgenerallyformed.Theeventualpurposeofthisstudyistoclarifytheunsteadyphenomenonoftheunderexpandedfreejetwhenthebackpressurecontinuouslychangeswithtime.ThecharacteristicoftheMachdiskhasbeenclarifiedinconsiderationofthediameterandpositionofitbythenumericalanalysisinthispaper.ThesonicjetoftheexitMachnumberMe=1isassumedandtheaxisymmetricconservationalequationissolvedbytheTVDmethodinthenumericalcalculation.ThediameterandpositionoftheMachdiskdifferswiththeresultsofasteadyjetandtheinfluenceonthecontinuouslychangingofthebackpressureisevidencedfromthecomparisonwiththecaseofsteadysupersonicjet.