Abstract A model is presented to predict the cross-flow displacement of a deep water marine riser or tether (tendon) due to vortex-shedding in a vertically sheared flow. The displacement of each mode is determined by a balance between the energy fed into the structure over lock-in regions of the structure and the energy dissipated by the fluid damping over the remainder. The mathematical formulation makes use of the vortex-resonance amplitude profile of the structure in a uniform flow. This profile is approximated by a polynomial which is based on experimental values of reduced velocity bounds for vortex lock-in as well as the reduced velocity at the peak lock-in amplitude. The profile is also directly predicted by using the wake-oscillator model. The drag coefficient is assumed to vary with the transverse displacement. The total amplitude response of the structure is calculated as a superposition of amplitudes of all excited vibration modes. A closed form solution is presented for the case of a riser or tether of uniform mass and cross-section under a uniform flow. The numerical results indicate that, as expected, more than one structural mode is usually excited when the riser or tether is subjected to a sheared flow. Moreover, an increase in shear parameter decreases the peak response amplitude but broadens the lock-in range over which large oscillation amplitudes occur; the virtual local drag coefficient can be significantly higher than the nominal value. It is found that the use of an average flow approximation to treat the sheared flow case may over-predict the vortex-excited motion amplitudes. The predictions show a reasonable agreement with limited reported experimental observations.