The effect of an equilibrium flow on resonant absorption of linear MHD waves in cylindrical magnetic flux tubes is studied in compressible viscous MHD. We treat the problem numerically with an application of the FEM combined with the Galerkin technique. The singularities of the ideal MHD equations are removed by incorporating a dissipative effect, namely the classical viscosity. We show that an equilibrium shear flow can significantly influence the absorption suffered by the incoming driving waves. The presence of an equilibrium flow may therefore be very determined for resonant absorption. A parametric analysis shows that there are values of the equilibrium velocity field for which the absorption rate becomes zero, even for rather small velocity shears. We also found negative absorption of wave power which apparently can be attributed to the resonant instability found by Hollweg et al. (1990). For other values of the equilibrium flow we find that the resonant absorption can be strongly enhanced, even up to total absorption of the incoming wave.