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A new Monte Carlo (MC) simulation method is developed for estimating the effective conductivity of random heterogeneous media. The method is based on the Itô formula for differentiable functions of diffusion processes, the similarity of the functional form of the generators of these processes and the operators of the steady state diffusion equation, smooth approximations of the conductivity field of multiphase heterogeneous media, and MC simulation. The article establishes the theoretical framework of the proposed method and gives estimates of the effective conductivity for a one-dimensional random heterogeneous medium with two phases. © 1997 American Institute of Physics.