Prior to any gasification in the underground coal gasification process, it is necessary to "link" or establish one or more relatively narrow high permeability channels between the injection and production well bores. Electrolinking achieves this permeability enhancement by carbonizing the coal via resistance heating between two electrodes placed in the well bores. This technique has been shown to be promising in commercial scale operations in the Soviet Union. However, field testing of this linking method in the US has indicated that it is unreliable and unpredictable. This paper develops a model based on linear stability theory which predicts the number, diameter, and propagation velocity of the electrolinks which form during the initial stages of electrolinking when the carbonization front is propagating radially about the electrodes. The model predictions are compared with limited data and then used to suggest possible improvement in this linking technique.