The Boundary Element Method (BEM), a numerical method developed in engineering fields, is capable of modelling complex geometrical domains. In this thesis, the BEM is described from an electrochemical perspective and applied to simulation of electrochemical systems. The properties of the BEM for electrochemical simulation are compared to the most common numerical methods used in electrochemistry and engineering fields; the Finite Difference Method, and the Finite Element Method respectively. The mathematical relation of these three methods is highlighted through a Weighted Residual formulation. Steady state diffusion at a generator-collector double microband for a diffusion limited reaction is used to validate a two-dimensional BEM model, and investigate mesh discretisation effects. Optimisation of the mesh and implementation of higher order boundary elements are reported. The two-dimensional steady state model is applied to simulate a variety of microband systems, including Inter-Digitated Arrays, realistic (imperfect) electrode geometries and a novel generator-collector microband array. An advanced variation of the BEM, the Dual Reciprocity Method (DRM), is described and applied to model a channel flow cell. Due to instability, the method is found inadequate to simulate this system. The details required to extend the DRM for transient systems are also described. The three-dimensional BEM is implemented and validated. The ability to model any three-dimensional domain has significant potential for simulation of complex geometrical systems in electrochemistry. The extension of the BEM to model multiple species and electrochemical mechanisms, and the future direction and relevance of the BEM as an electrochemical simulation method, are discussed.