We suggest a new approach for evaluating the dynamic response of existing embankment dams as a guideline for national engineering regulations in Serbia. This novel concept is applied to the case study of the existing embankment dam “Zavoj” (Serbia), built at the place of the previously formed natural dam (due to large landslide activity), and exposed to Mw7.4 Vrančea earthquake and under double impact of Kresna earthquake (Mw6.8 and Mw7.1). Results of transient FEM and direct dynamical analysis of the three-dimensional FEM model of the “Zavoj” dam indicate that the existing dam is stable in dynamic conditions, while the surrounding terrain is either on the verge of stability or becomes unstable, depending on the assumed geotechnical conditions and a relevant earthquake analyzed. As a result, we construct a landslide hazard map in dynamic conditions and the dam damage map, which enables the identification of unstable, damaged, or weak parts of the dam, its immediate surroundings, and the accumulation zone in general. The results indicate that direct dynamical analysis is obligatory when two succeeding earthquakes occur and temporal evolution of displacements in the model is required. Additionally, the application of the remaining bearing capacity criterion indicates a much larger zone of potential instability compared to the extent of equivalent plastic strain and the location of the old sliding surface. By following the proposed guidelines, one secures the inclusion of all the relevant influential factors in the comprehensive dynamic analysis of existing embankment dams, leading eventually to reliable decisions on further design, (re)construction, and/or monitoring activities.