A dam is a massive structure built to block the flow of water in a river or stream, creating a reservoir. The water stored in the reservoir can be used for various purposes such as generating electricity, irrigation, and drinking water. Dams come in different types, but one of the most durable and reliable types is the gravity dam. It is built mainly with concrete and designed to hold back water using its weight. The upstream side is where the water flows in, while the downstream side is where it flows out. The safety of a gravity dam is analyzed through the First-Order Reliability Method (FORM) which determines the probability of failure or safety index. The study shows that the safety factor and reliability index decrease as the dam height increases or as the dam slope increases at a constant height. Additionally, the upstream slope of earth core rockfill dams has higher safety factors and reliability indexes than the downstream slope, making the latter the critical failure mode.