An X-ray stress measuring technique - pseudo-ψ angle changing method- is proposed to measure circumferential stress on a concave cylindrical surface at a narrow part. To avoid X-ray interception by a side wall, X-ray irradiation and detection are conducted in a plane parallel to the plane including the central axis of the cylindrical surface (the configuration of axial stress measurement by the iso-inclination method), and the diffraction angle at ψ=0deg is measured on an inclined surface (part of the cylindrical surface). This measurement is conducted on five or more irradiation positions changed along the circumference of the cylindrical surface by moving a measured object, keeping the attitude of the object fixed, in the direction of the normal of the plane including the X-ray path. The position change causes the shift of diffraction peak since the angle between the normal of the irradiated area and incident X-rays changes according to the position, i.e. the position change is equivalent to the change of ψ angle in the conventional sin 2 ψ method. The circumferential stress is obtained from the relation between the irradiation position and the diffraction angle at ψ=0deg. To examine the validity of pseudo-ψ angle changing method, residual stress in the tooth depth direction at the tooth root of a rack was measured using this method and the conventional method respectively. The measured values of the stress by two different methods were in good agreement.