We explore the concept of effective hydraulic conductivity for a bounded randomly heterogeneous formation under steady-state flow regime. The novelty of our study consists of establishing a tensorial nature of the effective conductivity. This occurs even for locally isotropic conductivity fields. Neuman and Orr  have demonstrated that stochastically averaged flow equations are non-local and non-Darcian, so that effective hydraulic conductivity does not generally exist. We derived our analytical expression for the effective conductivity tensor by localizing these equations, and assessed the accuracy of this approximation by comparing the resulting hydraulic heads and fluxes with their non-local counterparts. Our solutions are in a good agreement with both recursive non-local finite elements results of Guadagnini and Neuman  and Monte Carlo simulations for mildly and strongly heterogeneous formations.