A fast algorithm to calculate the response of uniaxial layered media on a rectilinear mesh is proposed in order to handle scattering phenomena due to inhomogeneities within them. The uniaxial layered media are with their optical axes parallel to the interfaces of the layered structure. The generalized Poisson summation formula is used to efficiently calculate the discrete Fourier transform of spatial responses of the layeredmedia from its continuous Fourier spectrum. Using the windowing technique, the integral involved in constructing the discrete Fourier spectrum can be performed in a small domain without compromising the accuracy of the result. Furthermore, a fast numerical integration method based on the recently proposed Padua points is used, which, together with the windowing technique, yields a fast solution to such scattering problems. Numerical simulations illustrate the accuracy and efficiency of the proposed algorithm.