PURPOSE: To produce a straight, stress corrosion cracking resistant stainless steel pipe, by applying solution heat treatment to austenitic stainless steel seamless pipe, and then straightening by using plural nonmetallic rolls under specified conditions.

CONSTITUTION: When straightening after solution heat treatment, the offset angle β°, bending angle γ°, and substantial crush amount α% expressed by substantial outside diameter change rate in % are variable conditions, while other conditions are set in average conditions. Under the straightening conditions of combinations within the region enclosed by three lines in terms of substantial crush amount and offset amount, namely, α=0.1, β=0.2, β=1.2-0.444α-0.71α2, the stainless steel pipe is straightened by using nometallic rolls such as hard rubber rolls. As a result, the residual stress in the outer circumferential direction of stainless steel pipe may be set to zero or compressive stress, so that occurrence of stress corrosion cracking may be prevented.