The　purpose　of　this　paper　is　to　study　the　local　well-posedness　problem　on　the　magnetohydrodynamics　(MHD)-structure　interaction　(MHDSI)　systems.　The　fluid　is　represented　by　the　incompressible　viscous　and　non-resistive　MHD　equation　in　Euler　coordinates　while　the　structure　is　modeled　by　the　elasticity　equation　with　superconductor　material　in　Lagrangian　coordinates.　The　equations　are　coupled　along　the　moving　interface　though　transmission　boundary　conditions　for　velocity,　stress　and　magnetic　field.　The　local　existence　of　at　least　one　strong　solution　in　time　to　the　incompressible　viscous　and　non-resistive　MHD-structure　interaction　model　was　proved　in　the　sense　of　one　suitable　Sobolev＇s　space　norm　by　using　the　careful　energy　method　and　fixed　point　theory　combining　with　penalization　and　regularization　techniques　and　by　overcoming　the　coupling　difficulties　caused　by　the　magnetic　field.　(C)　2020　Elsevier　Inc.　All　rights　reserved.