Thetransientflowmathematicalmodelofarbitraryshapedheterogeneousreservoirswithimpermeabilitybarrierisproposedinthispaper.Inordertoestablishthismodel,theperturbationmethodisemployedandthesolutionofmodelisexpandedintoaseriesinpowersofperturbationparameter.ByusingtheBoundaryElementMethod(BEM)andDuhamelprinciple,wellborepressurewitheffectsofskinsandwellborestorageisobtained.Thetypecurvesareplottedandanalyzedconsideringeffectsofheterogeneity,arbitraryshapeandimpermeablebarriers.Finally,theresultsobtainedbyperturbationboundaryelementmethodiscomparedwiththeanalyticalsolutionandisavailableforthetransientpressureanalysisofarbitraryshapedreservoirs.