A number of models are used to describe the function of the static mercury drop electrode (SMDE). A modified version of the Cottrell equation is shown to be effective in predicting the diffusion-controlled current as a function of time. A more rigorous and general treatment using digital simulation is also developed. The unique valve-controlled operation of the electrode is found to create a complex hydrodynamics problem. Discrepancies between theoretical and experimental results are found to result mainly from the complex hydrodynamics.