Abstract The effects of process conditions on the dimensional accuracy of tubes in cold pilgering were studied. The dimensions included the ovalities of the outer and inner diameters and the eccentricity ratio of the wall thickness. The permissible variations of the dimensions on the objective tubes were of 10 μm order. The process conditions included the feed rate (1.0, 1.5, 2.0, and 2.5 mm/stroke), stroke speed (140, 180, and 200 strokes/min), and turn angle (40, 60, and 80°). The materials tested were type 316L stainless steel and the zirconium alloy Zircaloy-4. The dimensions of the tubes were measured by ultrasonic and laser equipment, and the characteristics of the tubes were determined, such as their hardness, tensile properties, residual stress, and crystallographic texture. The dimensions of the tubes being subjected to cold pilgering were continuously measured by ultrasonic equipment. Strong effects of the feed rate and turn angle on the ovality were observed; the ovality increased with the feed rate. The increase in ovality was thought to be caused by springback. The mechanism underlying the increase in ovality with the feed rate is described by considering the inhomogeneous springback after releasing the tubes from the constraint of the tools. The effect of the turn angle on the ovality was proved to be related to the asymmetric deformation of the tube from the numerical analysis results of cold pilgering. The effect of the springback on the ovality was confirmed by the measurement results for the residual stress. The eccentricity ratio of the wall thickness was unaffected by the process conditions; it was mainly determined by the eccentricity ratio of the mother tube. The eccentricity ratio of 316L tubes decreased after cold pilgering, whereas that of Zircaloy-4 tubes increased. The change in the eccentricity ratio was explained by a self-centering mechanism based on the combined effect of the roll dies and mandrel, and the eccentricity ratio of Zircaloy-4 tubes was proved to be related to the mechanical anisotropy owing to their crystallographic texture. These findings are expected to assist the selection of manufacturing conditions for tubes with close tolerance.