A theoretical study is carried out for investigating spatial instabilities of a supersonic vortex sheet inside a circular duct. The sheet is cylindrical in shape, separating the flow into an inner region and an outer one of uniform properties. It is found that there is one family of subsonic (Kelvin–Helmholtz) instability waves which are accompanied by two families of neutral modes. Two families of supersonic instability waves can be identified to be associated with two other families of neutral modes. A mathematical analogy indicates that instability modes at high frequencies bear resemblance to those obtained by Tam and Hu [J. Fluid. Mech.203, 51 (1989).] for plane mixing layers inside a rectangular channel. Geometric effects of both the vortex sheet and the outer confinement are significant only at relatively low frequencies of disturbances. In addition, extensive parametric study reveals interesting features of the dependence of the instability waves on the density ratio, velocity ratio, radius ratio of the inner and outer regions, and three‐dimensional disturbances.