The use of pseudo-static procedures to evaluate the seismic stability analysis of slopes of a tailings storage facility (TSF) and a mine waste dump (MWD) is a common practice in geotechnical engineering; however, new methodologies have emerged for the calculation of seismically induced permanent displacements of earth structures, which is considered a more reliable approach compared to the calculation of a factor of safety (FOS) obtained by the pseudo-static procedure. The authors have studied the application of several methodologies to evaluate the seismic stability of TSFs and MWDs based on two case studies. As part of these applications, slope stability and one-dimensional (1D) nonlinear seismic response analyses were performed. Cyclic laboratory tests were performed on coarse tailings and mine waste to evaluate their dynamic properties and compared with current state-of-the-practice literature curves. The resulting displacements using these procedures proved to be, in general, similar. This research suggests that seismic analysis should be less focused on the pseudo-static FOS as a parameter to predict the seismic stability of TSFs and MWDs, unless a rational criterion is chosen for the determination of the seismic coefficient.