This article establishes a three-dimensional fluid-structure interaction (FSI) model for reciprocating rod seals. Based on this model, a novel method using a two-dimensional FSI model to solve the average sealing performance across multiple sections is proposed for the first time. This method allows for the dimensional reduction of solid mechanics, contact mechanics, and fluid mechanics analysis. The performance of the sealing system was calculated and analyzed under static eccentricity (which does not change with piston rod motion) and dynamic eccentricity (which changes with piston rod motion) using the aforementioned models. The results indicate that the sealing performance calculated by both models is highly consistent, demonstrating that, within the permissible engineering limits, the two-dimensional FSI model can replace the three-dimensional model, thereby reducing computational costs and improving convergence. Additionally, the results show that eccentricity increases the friction and leakage rates of the sealing system, with dynamic eccentricity having a greater impact on sealing performance than static eccentricity due to the viscoelasticity of the rubber.