Long distance ore concentrate pipeline leaks are characterized by a rapid release of significant amounts of slurry. Such spills most often occur at cross-country locations with scarce or no immediate containment facilities available. The subsequent flow is driven by topographic conditions and the result of the interaction between time-dependent boundary conditions, given both by the rupture itself and the location of the event. In the present paper, the relevance of contingency plans including response team times and locations at some critical points to stop the spreading of an iron concentrate leak is discussed in terms of a set of spill run-out computations. For this purpose, the set of numerical simulations of vertically averaged momentum and continuity equations assuming two different topographic conditions, various rhological parameters for the slurry and constant discharge curves are considered. The slurry, modelled following the Herschel-Bulkley model, behaves as a viscous mixture with a small yield stress, where the parameter choice follows the characteristics of a typical iron ore concentrate. The numerical model, receives the topography from a DEM (Digital Elevation Model), the rheological characteristics of the slurry and a discharge curve, consisting of a time sequence of the incoming flow at a specified location and characteristics for the Herschel Bulkley model obtained by a previous rheology test as inputs. Results suggest the need to use a non-Newtonian model rather than the simpler water-over-rough topography approach using a Manning coefficient, most commonly found in two-dimensional numerical approaches. Implications both on the flow spreading and the characteristic times required for emergency team response are discussed in the light of two different topographies, representing mild and strong sloping terrains.