Acomprehensivetreatmentoffractureoffunctionallygradedmaterials(FGMs)isprovided.Itisassumedthatthematerialpropertiesdependonlyonthecoordinateperpendiculartothecracksurfacesandvarycontinuouslyalongthecrackfaces.Byusingalaminatedcompositeplatemodeltosimulatethema-terialnon-homogeneity,analgorithmforsolvingthesystembasedonLaplacetransformandFouriertransformtechniquesispresented.Unlikeearlierstudiesthatconsideredcertainassumedpropertydistributionsandasinglecrackproblem,thecurrentinvestigationstudiesmultiplecrackproblemintheFGMswitharbitrarilyvaryingmaterialproperties.Transientthermalstressesarepresented.