This　paper　studies　directional　Holder　regularity　of　two-variable　functions　by　their　shearlet　coefficients,　where　the　shearlets　are　defined　by　Guo　and　Labate　(2013).　We　provide　necessary　conditions　for　a　function　possessing　some　directional　Holder　regularity　and　the　corresponding　sufficient　conditions,　motivated　by　the　work　of　Sampo　and　Sumetkijakan　(2009)　and　Lakhonchai　et　al.　(2010).