The power law hardening constitutive relations for porous material were established by the material yield function. An idealized interface fracture model was established in which the indenter as rigidity was embedded in the porous material. Under the condition of plane strain, through the analysis of the singularity of the stress and strain and combining the motion and compatibility equations, the governing equation of the wedge-tip was deduced. With the help of numerical calculations and boundary conditions, the asymptotic solutions of the stress and strain near the wedge-tip were obtained. Finally, the influence of the material constants α (pressure sensitive coefficient), the angle of the indenter and the interfacial friction on the fracture of the porous material was discussed.