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A numerical solution for the eigenvalue in a frictional punch problem is presented, One edge of a concave notch is assumed to be traction free, and the other edge is in contact with the frictional punch (Fig, 1), In addition to the normal pressure the friction force is also applied along the contact edge of punch. The friction coefficient δ is assumed within the range −0.3 ≤ 6 ≤ 0,3. The notch angle β between two edges is varying within the range π ≤ δ ≤ 2π. The target function method is used to evaluate the eigenvalue λ1 in the stress expression σij ≈ O(1/rλ1). Finally, the obtained eigenvalues are expressed in the form of λ1 = s(δ, β). The pressure under punch and the stresses at the corner points are singular in general.