The effect of wall surface roughness on the fluid mass flow rate through a nano slit pore in the Poiseuille flow was analytically studied by using the flow factor approach model. One wall surface was perfectly smooth and the other coupled wall surface was periodically distributed with rectangular protrusions or dents. Weak, medium-level and strong fluid-wall interactions were respectively considered. It was shown that even the wall surface protrusion with a small height significantly reduces the mass flow rate through the channel in spite of the fluid-wall interaction; this effect is especially significant for a strong fluid-wall interaction. The increase of the width of the wall surface protrusion also significantly reduces the mass flow rate through the channel. The effect of the wall surface protrusion is weakened with the increase of the channel height. The wall surface dent was found to increase the mass flow rate through the channel and the mass flow rate is enhanced with the increases of both the depth and the width of the dent. This effect is more significant for a stronger fluid-wall interaction. However, for deep dents, the effect of the wall surface dent on the mass flow rate is almost independent on both the depth of the dent and the fluid-wall interaction. While for narrow dents, the effect of the wall surface dent is negligible in spite of the fluid-wall interaction. The effect of the wall surface dent is also weakened with the increase of the channel height. (C) 2016 Elsevier Ltd. All rights reserved.