Despite excellent sealing capabilities, rubber materials present challenges due to their creep behavior, which substantially affects mounting edge sealing performance. Finite element analysis is employed to evaluate and optimize flange mounting edges with rubber gaskets, focusing on contact gap minimization and tensile stiffness enhancement. The research methodology encompasses three phases: developing a computational model based on experimental rubber creep data; creating a finite element model to assess parameter influences on sealing and mechanical properties; and implementing a multi-objective optimization framework utilizing mounting edge thickness, rubber elastic modulus, and bolt preload as design variables. Results reveal that increasing all three parameters reduces contact gaps and improves sealing performance, with higher preload force particularly effective at mitigating creep-induced degradation over time. The optimization analysis indicates that mounting edge thickness exerts the most significant influence on performance metrics, followed by bolt preload, while rubber elastic modulus has comparatively minor effects. The optimized design achieves substantial improvements in both tensile stiffness and sealing effectiveness through reduced contact gaps.