A Fast Fourier Transform (FFT) based method for computing the dynamic permeability of periodic porous media is presented. The flow is described by the linearized Navier-Stokes equations in the presence of an oscillatory pressure gradient across the domain. The method of resolution uses an iterative scheme and exact expressions for the dynamic Green’s tensor in Fourier space. The accuracy of the approach is assessed through comparisons with ah exact solution, in the case of the flow in a cylindrical tube and with available numerical data provided in the literature for the case of flow through regular arrays of spheres or ellipsoids.