As the cylinder of a given length, worked and treated with heat, is liable to conples deformation by the residual stress due to boring, the author studied the residual stress as a two dimensional problem. As Sachs' formulas, which are commonly used, hold good only when d
p is infinitely small, the author tried to deduce the formulas representing the mean of each of the three internal stresses when Δ
p is finite. These formulas will give the stresses of the central part and may also be applied to solid cylinders. The correction formulas, obtained by comparing Sachs' with the author's, show the difference between d
p and Δ
p, and also indicate that the values of the internal stresses near the central part, calculated by Sachs'formulas, need some corrections.
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