The paper examines the instability of a complex-shaped circumferential crack in a Type 304 stainless steel pipe that is subjected to rotations at the pipe ends. A through-wall crack extends over a prescribed fraction of the pipe circumference, while there is also an internal circumferential crack extending around the remainder of the pipe section. Instability of circumferential growth of the through-wall crack segment is examined using a crack tip opening angle growth criterion, and an assessment is made of the effects of crack configurational parameters, pipe size and material properties, on the instability criterion. The paper highlights the undesirability, from a safety perspective, of having a complex-shaped crack in a region with adverse fracture resistance characteristics.