Reliable attachment ability of insect adhesive pads is proposed to be due to pad secretion. It has been shown that surface roughness strongly reduces adhesion forces of insect pads. This effect has been explained by decreased contact area and rapid fluid absorption from the pad surface by rough surfaces. However, it remains unclear how the fluid flows on rough substrates having different roughness parameters and surface energy. In this paper, we numerically studied the fluid flow on rough substrates during contact formation. The results demonstrate that an increase in the density of the substrate structures leads to an increase in fluid loss from the pad: substrates with a fine roughness absorb pad fluid faster. Decreased affinity of the solid substrate to the fluid has a more remarkable effect on the fluid loss and leads to a decrease in the fluid loss. With an increase in the aspect ratio of the substrate irregularities (porosity), the fluid loss is decreased. The numerical results obtained agree well with previous observations on insects and experimental results on nanoporous substrata. The significance of the obtained results for understanding biological wet adhesives is discussed.