Boththeinplaneandout-of-planetransversevibrationsofaviscoelasticcablesubjectedtoaninitialstressdistributinguniformonthecrosssectionarestudied.Theconstitutionofthecablematerialisas-sumedtobeofthehereditaryintegraltype.Thepartialdifferential-integralequationsofmotionarederivedfirst.ThenbyapplyingGalerkin’smethod,thegoverningequationsarereducedtoasetofsecond-ordernon-lineardifferential-integralequationswhicharesolvedbyfinitedifferencenumericalintegrationprocedures.Finally,theeffectsoftheviscosityparameterandtheelaslicparameteronthetransientamplitudesofthefirstmodeareinvestigatedbynumericalsimulation.