Gas drainage is one most important technical measure of controlling gas for high gassy coal mines, and the state of stress-strain is closely related to the stability of surrounding rock of borehole. The Yield criterion is the principal condition for judging the plastic of surrounding rock. M-C criterion and D-P criterion, which are widely used in numerical simulation，are basically related with the influences such as cohesive force, internal friction angle, in-situ stress and so on. However, these criterions have different functions and yield surface, especially without considering the mid-principal stress effect for Mohr-Coulomb yield criterion. Thus, elastic-plastic analysis of surrounding rock on gas drainage borehole under various yield criterions are proposed for comparing the effect of different mechanic characteristics of surrounding rock on the stress and displacement of elastic-plastic zones and the radius of plastic zone. And the results are preferably used for choosing a suitable yield criterion for the model calculations according to the different surrounding rock characteristics, in order to ensure the security of gas drainage engineering practice even better.