Grid line deformations produced in two dimensional flow-type machining of metals of various strain-hardening characteristics are compared with those of Kudo's solutions. In slow speed machining, the solutions fail to account for plastic deformation arising from the pre-flow region, which always appears regardless of strain-hardening in work materials, although they appear to be in success for explaining chip curl and secondary flow along tool-face. In high speed machining, on the contrary, the theoretical patterns using velocity discontinuity appear to be in good agreement with experimental patterns due to disappearance of the pre-flow region. It is also interesting that Kudo's solution with frictional stress of k, maximum shear stress, along whole tool-chip interface does realize in high speed machining.The permissible range of Kudo's solution in the plot of φ against β-α, where φ, β and α are shear angle, friction angle and rake angle respectively, is determined by using the restrictions of possible frictional stres distribution, mass continuity and Hill's theorem. While the range covers almost all of Merchant and Lapsley's experimental results, it is unsuccessful to cover the results in slow speed machining. The reason may lie in the incompleteness of the solutions for explaining the pre-flow region.Some new slip line solutions involving the pre-flow region are proposed in order to cover the slow speed machining data, although they are not complete in theoretical point of view.