  An anisotropic random barrier model is presented, in which the transition
probabilities in different directions have different probability density
functions. At low temperatures, the anisotropic long--time diffusion
coefficients, obtained using an effective medium approximation, follow an
Arrhenius temperature dependence, with the same activation energy for each
direction. Such activation energy is related to the anisotropic percolation
properties of the lattice, and can be analysed in terms of the critical
percolation path approximation. The anisotropic effective medium approximation
is shown to predict the correct percolation threshold for an anisotropic
two--dimensional square lattice. In addition, results are compared with
numerical simulations using a fast kinetic Monte Carlo algorithm.
