The role of interfacial shear in the onset of instability of a cylindrical viscous liquid jet in a viscous gas surrounded by a coaxial circular pipe is elucidated by use of an energy budget associated with the disturbance. It is shown that the shear force at the liquid–gas interface retards the Rayleigh-mode instability which leads to the breakup of the liquid jet into drops of diameter comparable to the jet diameter, due to capillary force. On the other hand the interfacial shear and pressure work in concert to cause the Taylor-mode instability which leads the jet to break up into droplets of diameter much smaller than the jet diameter. While the interfacial pressure plays a slightly more important role than the interfacial shear in amplifying the longer-wave spectrum in the Taylor mode, the shear stress plays the main role of generating the disturbances of shorter wavelength.