Flow in a porous medium with a random hydraulic conductivity tensor (K) over bar (x) is analyzed when the mean conductivity tensor (K) over bar (x) is a non-constant function of position x. The results are a non-local expression for the mean flux vector (q) over bar (x) in terms of the gradient of the mean hydraulic head <()over bar>(x), an integrodifferential equation for <()over bar>(x), and expressions for the two point covariance functions of q(x) and phi (x). When K(x) is a Gaussian random function, the joint probability distribution of the functions q(x) and phi (x) is determined.