In this paper, we study kink and sausage oscillations in the presence of longitudinal background flow. We study the resonance absorption of kink and sausage modes in the slow continuum, under magnetic pore conditions, in the presence of flow. We determine the dispersion relation, and solve it numerically to find the frequencies and damping rates of the slow kink and sausage surface modes. We also obtain an analytical solution for the damping rate of the slow surface mode in the long wavelength limit. We show that in the presence of plasma flow, resonance absorption can result in strong damping for forward waves, and can be considered as an efficient mechanism to justify the extremely rapid damping of slow surface sausage waves observed in magnetic pores. Moreover, the plasma flow reduces the efficiency of resonance absorption to damp backward waves. With respect to pore conditions, resonance instability is avoided in our model.
