The work deals with the problem of fabricating new materials for modern devices of microelectromechanics, microelectronics, biomimetics, etc. using the local electrodeposition of metals. The mathematical model is developed for the formation of 3D microstructures (microcolumns) by the local electrochemical deposition of metal using a moving disk microanode. The numerical solution of the mathematical problem is performed using the finite element method on the irregular grid. The grid is deformed and adaptively remeshed during modeling of deposit growth. Evolution of deposit surface is calculated for various exchange current densities, transfer coefficients, interelectrode distances and various dependences of the current efficiency on the current density. The results of modeling allow one to determine the relationships between the parameters of electrodeposition and the shape and dimensions of formed microstructures. These data can be used to predict the results of local electrodeposition of metal and to optimize the operation conditions. (C) 2018 Elsevier Ltd. All rights reserved.