The　WentzelKramersBrillouin　method　is　employed　to　study　the　cut-off　frequencies　of　the　horizontal　shear　waves　in　a　freestanding　functionally　graded　piezoelectricpiezomagnetic　material　film　with　the　electrically　and　magnetically　open　boundary　conditions.　An　analytical　solution,　which　could　be　used　in　analyzing　the　problems　of　various　functionally　graded　materials,　is　proven　to　have　high　precision　by　analytical　analysis　and　a　numerical　example.　The　results　reveal　that　the　set　of　cut-off　frequencies　is　a　series　of　approximate　arithmetic　progressions.　A　theoretical　foundation　based　on　the　relationship　between　the　cut-off　frequencies　and　the　materials　gradient　property　is　established　for　nondestructive　evaluation.