At high cutting speeds, self-excited regenerative vibrations (“chatter”) of drilling and reaming tools may occur. Chatter is an instability in which oscillation of the tool causes variation in the chip load, which in turn amplifies tool motion. This phenomenon is well known in turning and milling, and has also been studied in boring. In drilling and reaming, both axial motion and radial (bending) motion of the tool may affect the chip load, but dynamic stiffness is often much higher axially. Analysis of radial chatter requires consideration of at least two degrees of freedom as well as consideration of the special geometry of the drilling and reaming tools. In this paper we find analytical stability boundaries for drilling; the analysis extends a boring model developed by Li and Ulsoy (1998). We also show that it is necessary to use a different approach to predict instability in reaming. Stability boundaries for reaming were found by a method proposed for milling by Altintas and Budak (1995). A dynamic time-domain simulation suitable for both drilling and reaming was used to confirm analytical predictions and obtain qualitative insight into the instabilities, which involve both forward and backward whirling modes.