Tailings dam breach analyses (TDBA) are essential in the mining industry for determining dam consequence classifications and developing emergency response plans. The 2021 CDA Technical Bulletin [1] on TDBA provides guidance on assessing tailings dam breaches, with particular attention to the presence of supernatant ponds and liquefiable tailings, which have a significant impact on the runout distance. The bulletin outlines four cases (1A, 1B, 2A, 2B) for TDBA, each accompanied by detailed step-by-step instructions. For cases 2A and 2B, numerical modelling techniques that account for large deformations can be employed to estimate the runout distance. These techniques are based on continuum mechanics, solving the mass and momentum equations. In geotechnical engineering, one of the numerical techniques that is gaining more attention to simulate large deformations is the material point method (MPM). While MPM offers the potential to evaluate damage following a tailings dam failure, the application of this methodology is limited in current engineering practice. Classical numerical approaches, such as the Finite Element Method (FEM), often results in mesh distortion, which makes them challenging to use in large deformations problems. In contrast, MPM is a particle-based method that employs material points (MPs) moving through a fixed mesh, thus avoiding the limitations of classical FEM to simulate flow-deformations problems. This paper applied the Material Point Method (MPM) to estimate the runout distance following the failure of two tailings storage facilities (TSFs) and a waste rock dump. Case 2A was applied to a TSF in Germany, while Case 2B was applied to both a TSF in Mexico and a waste rock dump in Peru. These scenarios demonstrate the capabilities of MPM in estimating the runout distance following dam failure. The results provide valuable insights to inform the discussions among dam owners, dam safety engineers, and regulatory authorities overseeing tailings dam management.