Electrical Resistivity Imaging (ERI) is one of the most used techniques in geophysics. As for many imaging methods, Digital Elevation Models (DEMs) are required to consider complex topography conditions. In this paper, we present some developments implemented into a new 3D-ERI software optimized in this context. The article focuses on the forward problem and discusses (i) the meshing methodology that directly consider DEMs in the processing and several profiles where electrodes are not necessarily aligned and (ii) new aspects for taking into account the unbounded domain. Indeed, defining boundary conditions of a numerical modelling problem arises as one of the most important issues into solving Partial Differential Equations (PDE). In order to solve the 3D-ERI forward problem, we propose an original implementation of the infinite elements, together with conventional finite elements. This methodology is first validated on synthetic case reproducing cliffs and, then, on a real case study presenting Badlands-like cliffs. Our results show that both the meshing procedure as well as the use of infinite elements enhance the efficiency of the forward problem as well as the accuracy of the inverse problem. In particular, this allows to reproduce more closely the local geology in complex environments than with a conventional 2D approach.