The Hoek-Brown (HB) strength criterion has been widely applied to the estimation of strength of intact rock and rock mass, whose yield function includes general form (a ≠ 0.5)and special form(a=0.5).In this work, a simple trail and error way to calculate the shear strength τ in the general case and an analytical expression of τ in the special case is developed using this criterion.Because of the HB strength criterion takes no account of the intermediate principal stress, Priest introduced a well-known three-dimensional HB criterion, further an analytical expression for effective yield stress σz is developed according to this three-dimensional criterion.Here, another two numerical ways as well as two explicit solutions to get σz using this criterion are proposed.Predications according to new methods agree well with the original results given by Melkoumian and Priest.