In the present paper are calculated and compared the stresses on the normal tools and the restricted tools which have three various rake angles by Least Square Method. The results obtained are summerized as follows. The tool displacement at rake angle .alpha. = 12 .deg. and .alpha. = 0 .deg. is positive value in the principal cutting direction and negative value in the feed direction. At rake angle .alpha. = -12 .deg. the displacement is negative value in both of directions. The principal stress of the restricted and normal tool is maximum at the tip of the tool, the shear stress is maximum after a certain distance from the tip. The result of FEM and P.E method shows that in the range of rapid decreasing of normal stress of the tool edge, the shear stress is maintaining a certain value. This is due to the friction characteristic of the chip.