The static contact characteristics of heavy-duty tracked vehicle roller and track plate contact structure are analyzed, and the influence mechanism of the roller's shape parameters on the contact stress is studied. According to the Hertz contact theory, a mathematical model of the roller and track plate contact is established. The contact structure model is established in ANSYS software, and the simulation results are compared with the Hertz theory results to verify each other. In the parameter optimization section for the roller and track plate, based on the Hertz stress calculation formula, a new method is proposed to establish a roller and track plate Kriging model and to globally optimize the model by the genetic algorithm (GA). After that, the relationship among the track roller radius R1, the track roller rim radius r1, and the track plate rim radius r2 is analyzed. The results show that the difference between the radius of the rim of the roller and the track plate and the radius of the roller rim both affect the maximum contact stress. Changing the plane contact into the curved surface contact can reduce the maximum contact stress by 33%. This study can provide a reference for the design and manufacture of supporting track rollers and track plates.