Understanding of the flow of fluids through beds of fibrous media is extremely important for composites processing. In this work, we have investigated a steady flow of a Newtonian fluid through two-dimensional porous media using lattice Boltzmann methods. The porous domains studied in this work represent different types of porous media encountered in composite processing. Initially, the methodology was validated with a simulation of flow through random porous media. Flow through porous media with circular and elliptical inclusions was simulated with different geometric arrangements. Simulations were also carried out with anisotropic porous media. The permeability was estimated as a function of porosity, geometric arrangements and the degree of anisotropy. The simulation results agree well with those from analytical, empirical and experimental studies. The results demonstrate that such a method will be very useful in simulating composite processing.