Numerical methods to compute double eigenvalues for circular ducts containing uniform and sheared flow are presented. A technique to verify both the maximum exponential decay and the double eigenvalue, impedance, and attenuation in ducts of different sizes are presented and discussed. For well cut‐on modes in a uniform‐flow duct, the impedance velocity by a simple relationship suggested in a previous study. However, in a sheared‐flow duct, optimum impedances are found to have much smaller values than in the uniform‐flow case.Subject Classification: [43]50.40; [43]20.45, [43]20.40.