Creeping flow through both regular and irregular screens was simulated by the lattice-Boltzmann method, and the dependence on screen porosity and Reynolds number of the pressure drop across the screen was analyzed. Regular structures were planar arrays of straight fibers or woven one-layer structures. The irregular planar structures were composed of randomly located and oriented fibers of finite length. A simple function of screen porosity based on partly numerical scaling arguments was found to describe accurately the simulated pressure drop across all regular screens. Due to their bigger surface area, the flow resistance of woven screens was found to be about 15% larger than that of regular planar screens with the same porosity. The pressure drop across irregular planar screens was found to be described by the same screen-porosity function with a slightly different ‘scaling’ exponent which thus appears to be dependent on the structure of the screen. The flow resistance of irregular structures was found to be clearly smaller than that of regular structures because of channelling of the flow through very few largest pores.