Seismic stability of tailings dams and embankments is an important topic which needs the special assessments by the researchers as it is mainly governed by the safety concerns. Several researchers in the past had attempted to investigate the seismic stability of earthen dams and embankments by using conventional pseudo-static method of analysis. However, the crude estimate of finding the approximate seismic acceleration makes the pseudo-static approach too conservative to adopt in the stability assessment. Although a few researchers in the recent past highlighted the limitations and drawbacks of the pseudo-static approach, there are very limited studies being reported worldwide for the seismic stability assessment of earthen dams and embankments by using alternative methods of analysis. In this paper, a recently developed and modified pseudo-dynamic method of analysis is used to compute the seismic inertia forces acting on the sliding wedge of the tailings dam by considering the effects of time of seismic accelerations, phase differences in the propagating shear and primary waves in the soil during an earthquake, frequency of earthquake excitation etc. with the horizontal and vertical seismic accelerations. The factor of safety decreases with increase in the seismic accelerations and phase difference in body waves. Influence of various parameters such as seismic acceleration coefficients, period of lateral shaking on seismic stability of tailings dam are studied under harmonic seismic loading conditions for both empty and full water cases. Present results are compared with the pseudo-static based solutions to validate the findings of the pseudo-dynamic method of analysis.