Plain Dutch weave and twilled Dutch weave meshes are superior filter media in terms of their high mechanical strength and tiny apertures. However, because they have high flow resistivity due to their complex flow paths, it is crucial to predict the pressure drop with high accuracy for a filtration process. We, therefore, investigated the effect of the aperture structure of a Dutch weave mesh on the flow resistivity. First, we proposed a calculation model for estimating the aperture size of a twilled Dutch weave mesh to thoroughly understand the aperture structure; whereas, the aperture structure of a plain Dutch weave mesh has already been clarified. Next, numerical simulations were performed using a combination of the lattice Boltzmann and immersed boundary methods. It was found that the drag force of the Dutch weave mesh increased at the inside aperture where the volume fraction increased, and in the twilled Dutch weave mesh, the drag force at the center also varied with the local torsion of the flow path. Based on these findings, we derived an equation for estimating the pressure drop across the Dutch weave mesh, and experimentally verified its validity. This enables a rational and highly accurate prediction of the pressure drop.