Hole drilling is a very common technique for measuring residual stresses. Adding an orbiting motion of the drill was found to improve hole quality in difficult to drill materials and has been in practice for decades. The orbiting motion affects the hole shape since the drilling tool cannot make a truly flat bottom unless the tool edges reach each part of the bottom, i.e. if the holes radius is twice the tool diameter. For instance, square-end end mills leave an inverted cone on the hole bottom, which has a systematic effect on the near-surface stresses unless the coefficients account for the non-cylindrical hole shape. This paper compares measurements made with tools of several sizes and different orbiting offsets and discusses the systematic effects found.