<p>This paper concerns the structural stability of cylindrical transonic shock solutions with nonzero angular velocity in a concentric cylinder. We establish the existence and uniqueness of such cylindrically symmetric transonic shock solutions and investigate the structural stability under axisymmetric perturbations of the incoming supersonic flow, the nozzle boundary conditions, and the exit pressure. The key elements are to utilize the Lagrangian transformation so as to straighten the streamline and employ the deformation-curl decomposition to convert Euler equations and the Rankine–Hugoniot conditions to a boundary value problem for the two second-order elliptic equations with a nonlocal term.</p>