This study comprehensively investigates the stress distribution and aging effects in Ethylene Propylene Diene Monomer (EPDM) and Liquid Silicone Rubber (LSR) gasket materials through a novel integration of hyperelastic modeling and advanced machine learning techniques. By employing the Mooney-Rivlin, Ogden, and Yeoh hyperelastic models, we evaluate the mechanical behavior of EPDM and LSR under conditions of no aging, heat aging, and combined heat and sulfuric acid exposure. Each model reveals distinct sensitivities to stress distribution and material deformation, providing unique insights into material degradation processes. Additionally, we utilize machine learning for predictive analysis, enhancing our understanding of stress responses and identifying critical aging effects. The findings offer practical implications for selecting suitable gasket materials and developing predictive maintenance strategies in industrial applications, such as fuel cells, where material integrity under stress and aging is paramount. This dual approach highlights the mechanical resilience and vulnerabilities of EPDM and LSR and opens avenues for real-time predictive analytics and material performance optimization.