Abstract：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 p plane and meridian lines show that the parabolic and hyperbolic type failure envelopes have no influences on the shape of the loci in the p 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.
