Abstract: The expressions of stresses in finite deformation of an elliptic or parabolic notch in infinite elastic plane has been obtained by incremental analysis. Such expressions are functions of loads, notch shape and material behavior. The stress singularity for a deep notch has especially been discussed, and it is found that this singularity could be related with the stress intensity factor in linear fracture mechanics, but the order of this singularity has been changed from 1/√ρ to α ln 1/√ρ, ρ being the curvature radiu of the notch root, α a material constant. The new result here explains the difference between the cases of plane strain and plane stress.