The effects of the microstructure of metal films on device performance and longevity have become increasingly important with the recent advances in nanotechnology. Depending on the application of the metal films and interconnects certain microscopic structures and properties are preferred over others. A common method to produce these films and interconnects is through electrodeposition. As with every process the ability to control the end product requires a detailed understanding of the system and the effect of operating conditions on the resulting product. To address this problem a three-dimensional on-lattice kinetic Monte Carlo (KMC) method is developed to conduct atomistic simulations of polycrystalline metal electrodeposition. The method utilizes the highly descriptive embedded-atom method (EAM) potential to accurately describe the interatomic interaction energy. The EAM potential is a semi-empirical multi-body potential that accounts for the cohesive forces in a metallic system. Its parameters are determined from known experimental data.In the presented study kinetically controlled copper electrodeposition onto polycrystalline copper under potentiostatic conditions is modeled using the aforementioned KMC method. Two plating modes are considered: direct current and pulsed-plating. Three surface processes are considered during electrodeposition: deposition dissolution and surface diffusion. In addition to the surface processes diffusion along grain boundaries is also considered. The KMC method presented in this study is capable of simulating the copper electrodeposition process at the atomic level over long time scales on the order of seconds. The computational requirement of these serial KMC simulations are a fraction (hours versus days) of that required by the parallel molecular dynamics (MD) approach to simulate the same process over the much shorter time scales on the order of nanoseconds. Consequently this KMC method allows for the simulation of electrodeposition processes over time scales that are experimentally-relevant and not feasible using MD.