The effects of an equilibrium flow in the internal regions of the Sun are studied on the damping of helioseismic f- and p-modes. The Sun is modeled as a multi-layered plasma, where the upper parts, representing the chromosphere and corona, are embedded in a horizontally unidirectional though vertically inhomogeneous magnetic field, while the lower part, representing the sub-photospheric polytropic region, is in a steady equilibrium state. The steady state sub-surface region can be considered as a first approximation of dynamic motions (e.g., differential rotation, sub-surface flows, meridional flows, convective motion, etc.). The frequencies and the line-widths of eigenmodes are affected by sub-surface flow and atmospheric magnetic fields. A key contribution to the effects comes from the universal mechanism of resonant absorption. When both atmospheric magnetic field and sub-surface flows are present, a complex picture of competition between these two effects is found. The theoretically predicted frequency shifts in a steady state show promise of explaining the observed effects. Changes in damping of f- and p-modes caused by changes (e.g. cyclic, if any) of steady state flows are predicted.