Abstract: Based on Ottosen’s discontinuous bifurcation solutions in elasto plasticity, the critical bifurcation directions and their corresponding hardening modulus for rocklike materials are derived. The two critical bifurcation directions on Mohr Coulomb and Drucker Prager criterion under uniaxial compression for different φ,ν are compared to each other.In addition to the traditional FEM, the bifurcation analysis is performed in a thin plate under compression and in an arch dam, and the computed localized elements show there is a shear failure zone in the plate and in the dam heel where the compressive stress is the maximum.