This study investigates the seismic performance of a concrete gravity dam and its associated spillway gates under far-field earthquake loading. Using advanced modelling techniques and SAP2000 software, the dam’s response to seismic events, including the Kobe, Tabas, and Chi-Chi earthquakes, is analysed. The study incorporates static and dynamic load cases, including seismic forces, hydrostatic and hydrodynamic pressures, and silt effects. Modal analysis reveals the dam's natural frequencies and vibration modes, while time history analysis assesses maximum displacements and stresses. The results indicate that the spillway gates are particularly sensitive to horizontal seismic forces, with larger displacements observed during high-frequency far-field earthquakes, especially the Kobe earthquake. The study highlights the importance of considering seismic forces in spillway design and offers valuable insights for improving dam safety under seismic conditions. Recommendations are made to enhance seismic resilience and ensure functional spillway performance during earthquake events.