The non-linear vibrations of a barrel, induced by the interaction with a high-speed moving projectile, negatively affect the shooting accuracy of a weapon. This study presents a new method that determines the non-linear behavior of the barrel with a passive vibration absorber and optimizes the absorber using the genetic algorithm (GA). Since both the barrel geometry and its coupling with the absorber are non-linear, a new finite element method (FEM) approximation has been developed for the interaction of barrel and projectile and combined with the classical finite element method. The final coupled equation of motion of entire system has been solved by a step by step integration, and for minimum tip deflection of the barrel, a GA has been then used in order to optimize the some parameters of the absorber. The results of analyses of the proposed FEM model were compared, and a good agreement was seen with the existing literature. In another example, the FEM–GA integrated optimization procedure was also used for the optimization of a passive vibration absorber, and a more accurate result (0.5% better) was obtained when compared to the experimental study given in literature.