The problem treated here is the steady state forced response of an infinitely long, viscoelastic cylindrical shell subject to an axially symmetric ring load which travels at a constant velocity. The shell is modelled by applying the correspondence principle to the refined theory derived by Herrmann and Mirsky [1]. The Fourier transform method in conjunction with the contour integral [2-4] has been applied to obtain the solution. A numerical illustration is given. The results of numerical calculations show that in the inverse Fourier transform the problem of improper integrals involving real poles (as in the undamped system) does not arise in the present study because the introduction of the damping mechanism moves the real zeroes away from the real axis in the frequency domain. Also, the results confirm the previous findings in the forced motions of viscoelastic shells [5,6] that the effects of rotatory inertia and shear deformation are insignificant. Further, the results show that for the load speed less than the critical speed, the internal damping causes a phase shift; for the load speed near the critical speed, the effect ofdamping appears to be quite pronounced; and for the load speed greater than the critical speed the two response curves start to merge from a certain point onward. The location of the merging point depends on the load speed.