We present a numerical study of the effect of the interfaces' roughness on layered media's upscaled elastic parameters. First, we consider a layered model with two types of elastic materials, assuming that the interfaces are not flat but rough, and apply the numerical upscaling technique to estimate the effective elastic properties of such models. After that, we apply a downscaling technique to reconstruct a layered media with flat interfaces but with uncertainties in elastic moduli of the layers. Next, we compute the covariance of the elements of the reconstructed stiffness matrix and prove that the logarithm of this matrix is linearly related to the logarithms of the standard deviation and the correlation length of the interfaces of the original problem. Finally, we use generated dataset to estimate covariance matrices of the stiffness matrix for arbitrary interface roughnesses.