Fluid　structure　interaction　(FSI)　gained　attention　of　researchers　and　scientist　due　to　its　applications　in　science　fields　like　biomedical　engineering,　mechanical　engineering　etc.　One　of　the　major　application　in　FSI　is　to　study　elastic　wall　behavior　of　stenotic　arteries.　In　this　paper　we　discussed　an　incompressible　Non-Newtonian　blood　flow　analysis　in　an　elastic　bifurcated　artery.　A　magnetic　field　is　applied　along　x　direction.　For　coupling　of　the　problem　an　Arbitrary　Lagrangian-Eulerian　formulation　is　used　by　two-way　fluid　structure　interaction.　To　discretize　the　problem,　we　employed　P2P1　finite　element　technique　to　approximate　the　velocity,　displacement　and　pressure　and　then　linearized　system　of　equations　is　solved　using　Newton　iteration　method.　Analysis　is　carried　out　for　power　law　index,　Reynolds　number　and　Hartmann　number.　Hemodynamic　effects　on　elastic　walls,　stenotic　artery　and　bifurcated　region　are　evaluated　by　using　velocity　profile,　pressure　and　loads　on　the　walls.　Study　shows　there　is　significant　increase　in　wall　shear　stresses　with　an　increase　in　Power　law　index　and　Hartmann　number.　While　as　expected　increase　in　Reynolds　number　decreases　the　wall　shear　stresses.　Also　load　on　the　upper　wall　is　calculated　against　Hartmann　number　for　different　values　of　power　law　index.　Results　show　load　increases　as　the　Hartmann　number　and　power　law　index　increases.　From　hemodynamic　point　of　view,　the　load　on　the　walls　is　minimum　for　shear　thinning　case　but　when　power　law　index　increased　i.e.　for　shear　thickening　case　load　on　the　walls　increased.