The　problem　of　elastic　stress　and　magnetic　field　concentration　near　the　vertex　of　a　compound　wedge　is　modeled　and　investigated.　The　wedge　is　made　of　two　isotropic　dielectric　soft-ferromagnetic　materials　and　is　immersed　in　a　static　magnetic　field.　The　technique　of　eigenfunction　series　expansion　is　applied　on　the　components　of　the　elastic　displacement　field　and　the　induced　magnetic　potentials　near　the　vertex.　It　is　shown　that　in　this　region,　the　magnetic　susceptibility　and　the　applied　magnetic　field　have　a　strong　influence　on　the　elastic　stress　and　magnetic　field　concentration.　The　results　are　instrumental　toward　actively　controlling　the　stress　concentration　intensity　via　the　applied　magnetic　field.　Copyright　©　2008　by　ASME.