We present a detailed physical and numerical model describing electrochemical behavior, aimed eventually at following the shape evolution in interfacial growth (electrodeposition in particular). Details of the numerical implementation are outlined, followed by a few telling examples of the electrochemical behavior at thin disk electrodes and at thick cylindrical electrodes. We demonstrate the large effect that radial mass transport has in the case of practically stationary thin electrodes, and the unusual behavior of propagating thin electrodes.