A　notch　correction　method　is　proposed　under　multiaxial　cyclic　loading,　in　which　the　real　stress　increments　can　be　directly　obtained　by　correcting　the　pseudo　stress　increments　at　the　notch.　Moreover,　the　proposed　method　does　not　inherently　restrict　the　direction　and　magnitude　of　real　backstress　increment　in　the　real　stress　space.　Additionally,　on　the　basis　of　Kanazawa　et　al.＇s　model,　the　proposed　method　utilizes　pseudo　notch　strains　in　replacement　of　measured　strains　to　take　account　of　the　additional　hardening　due　to　the　non-proportionality　of　external　loadings.　Based　on　the　proposed　correction　method　integrated　with　constitutive　equations　using　Garud＇s　hardening　model,　a　notch　stress-strain　estimation　methodology　is　developed　to　calculate　the　local　elastic-plastic　stress-strain　responses　at　the　notch　area.　The　presented　methodology　does　not　require　iteration.　The　applicability　of　the　presented　methodology　was　verified　by　the　experimental　data　of　TC21　titanium　alloy　notched　tubular　specimens　in　this　study　and　SAE　1070　steel　notched　shaft　specimens　from　the　literature.　The　results　showed　that　the　calculated　notch　strains　correlate　well　with　the　measured　strains　under　proportional　and　non-proportional　loadings.　(C)　2017　Elsevier　Ltd.　All　rights　reserved.