Analysis　of　the　Mohr　circles　proves　that　the　original　two-parameter　double　shear　unified　failure　criterion　has　the　linear　type　failure　envelope,　and　the　improved　failure　criteria　with　parabolic　and　hyperbolic　type　failure　envelopes　are　given　out　in　order　to　describe　the　rock　failure　properties,　especially　the　rock　tensile　property　better　than　the　original　one.　Analyses　of　loci　in　the　π　plane　and　meridian　lines　show　that　the　parabolic　and　hyperbolic　type　failure　envelopes　have　no　influences　on　the　shape　of　the　loci　in　the　π　plane,　but　the　shape　of　the　meridian　lines　are　changed　from　straight　lines　to　curved　lines.　The　limit　surfaces　of　the　improved　criteria　are　paraboloid　or　hyperboloid　in　the　principal　stress　coordinates.　Distances　from　the　conic　points　to　the　original　coordinate　point　are　smaller　than　those　using　the　linear　type　failure　envelope.　Cone　sizes　among　the　criteria　using　three　different　envelopes　are　the　criteria　with　parabolic　type　failure　envelope　being　the　smallest,　with　hyperbolic　type　failure　envelope　being　the　second,　and　with　linear　type　failure　envelope　being　the　largest.