The boundary element (BE) method is presented as an efficient and powerful method for the analysis of electrochemical processes. The paper describes the theory and numerical details required to develop steady state, one-, two-, and three-dimensional diffusional models for voltammetric simulations. The reduction in dimensionality brought about by the application of BE method for processes is noted, along with the resulting benefits when applied to electrochemical systems. The versatility and efficiency of the numerical procedures are examined with respect to a number of electrode geometries. In the case of 2D procedures the simulation of a microdisk and microhemispherical geometries are evaluated and the results compared to the analytical behavior. The change in current density observed as the hemispherical electrode is sequentially flattened to a microdisk is then described. Three-dimensional simulations focus on modeling a microdisk electrode which is then distorted. The resulting current density obtained for a range of three-dimensional geometries are noted. The potential of the BE method for examining irregular electrode geometries is also noted.