To evaluate the effects of wettability, pore geometry and the saturation history on the electrical conductivity of rocks, a three dimensional pore network model has been developed. The effective medium theory is used to simulate the electric and hydraulic conductance in this network. Each element in the network is assumed to consist of a converging-diverging pore with cylindrical cross section. A pore throat size distribution, an aspect ratio and the degree of pore connectedness characterize the pore structure. An electrically conducting thin film of water is allowed to exist on the pore walls in a strongly water wet medium. The accessibility properties of the 3-d network are approximated by a Bethe tree with the same percolation threshold. Results show that in strongly water wet media saturation exponents (n) between 1 and 2 can be obtained depending on the pore geometry parameters chosen. More highly connected pores lead to smaller values of n. In the limit of a capillary tube, n goes to 1. 0. For oil-wet systems, much larger n values, between 2 and 5 are obtained. For the water-wet case and for imbibition in the oil-wet case the resistivity index (1) vs. saturation (Sw) plots are concave upward indicating e increasing values of n while for drainage in the oil-wet case I-SW curve is convex upward indicating decreasing values of n at lower water saturation. Wettability is seen to have the most significant effect on the resistivity behavior. The variation between water-wet and oil-wet rocks decreases as the pore connectivity increases. For a strongly water-wet case the inclusion of electrical conduction through thin wetting films causes the I-SW curve to become convex upward. This is also to be expected when surface conduction plays a role as is the case in shaly sands. Hysteresis effects are found to be small for water wet systems. However in oil-wet cases, values of n for imbibition are found to be significantly higher than those for drainage at low water saturations. Hysteresis effects become more pronounced as the pore connectivity decreases. Other pore geometry factors such as pore aspect ratio and pore size distribution are also shown to have a significant effect on the saturation exponent. A comparison between the theoretical trends and experimental observation provides a better insight into the mechanisms of electrical conduction in complex pore geometries. For example, bimodal porosity systems are shown to display a break in the slope of an I-SW plot corresponding to the relative fraction of pore spaceoccupied by small and large pores.