Given the sustained mineral-deposits ore-grade decrease, it becomes necessary to reach greater depths when extracting ore by open-pit mining. Steeper slope angles are thus likely to be required, leading to geomechanical instabilities. In order to determine excavation stability, mathematical modelling and numerical simulation are often used to compute the rock-mass stress-state, to which some stability criterion needs to be added. A problem with this approach is that the volume surrounding the excavation has no clear borders and in practice it might be regarded as an unbounded region. Then, it is necessary to use advanced methods capable of dealing efficiently with this difficulty. In this work, a Dirichlet-to-Neumann Finite Element Method (DtN-FEM) procedure is applied to calculate displacements and stresses in open-pit slopes under geostatic stress conditions. which was previously devised by the authors to numerically treat this kind of problems where the surrounding domain is semi-infinite. Its efficiency makes possible to simulate, in a short amount of time, multiple open-pit slope configurations. Therefore, the potentiality or this method for open-pit slope design is investigated. A regular open-pit slope geometry is assumed, parameterised by the overall-slope and bench-face angles. Multiple geometrically admissible slopes are explored, and their stability is assessed by using the computed stress-field and the Mohr-Coulomb failure criterion. Regions of stability and instability are thus explored in the parametric space, opening the way for a new and flexible designing tool for open-pit slopes and related problems.