In this paper the electrical conductance of a two-phase composite medium with ellipsoidal inclusions has been investigated by using the effective-medium theory(EMT). An anisotropic factor m is suggusted TO take account of the local anisotropy of an inhomogeneous system. A formula for calculating the effective electrical conductivity tensor in such case has been proposed. A geometrical structure factor Ii(i = x,y,z) is introduced to estimate the near field effect between the particles aggregated in the inclusions. It has been shown that there is a simple relation between the structure factor Ii and the depolarization factor ni. The calculated results based on the EMT show that prolate ellipsoid (b/a = 0.2) and oblate ellipsoid (b/a=7.5) are the two principle geometrical configurations leading to the percolation threshold c1* =0.17. A preliminary theoretical analysis informs that the common mechanism leading to the percolation by these two configurations is the formation of an 'infinite' chain-shaped cluster.