The generalized Hoek-Brown yield surface presented in principal stress space resembles a conical yield surface whose normal section on deviatoric plane ($pi$-plane) is an irregular hexagon with sharp comers. This yield criterion is singular in six corners (apices) and regular in all other locations. These singular points, tangent of yield surface is indeterminate, occur at the locations where Lode angle approaches to $pm30$ degrees. The yield locus is convex and possesses similar shape as Mohr-Coulomb yield surface. Due to the presence of singular points, the direction of plastic straining is indeterminate and thus elastic-plastic constitutive matrix cannot be formed at those locations. In order to overcome this difficulty the generalized Hoek-Brown yield locus is explicitly defined using circular cone where the circle coincides with the outer and inner apices of the Hoek-Brown hexagon at any section. In this paper, detailed procedure is outlined to construct elastic-plastic constitutive matrix using generalized Hoek-Brown and modified yield surfaces with non-associated flow rule. Finite element analysis is performed with an example of two-dimensional circular opening under plane strain condition to compare these two yield criteria in terms of stresses and displacements.