As an important part of long-range nondestructive testing and structural health monitoring technology, ultrasonic guided wave technology has been used in a wide range of applications in aerospace, petrochemical, transportation, and other fields. This paper extends the previously developed wave finite element method by introducing the prestressing effect in Murnaghan hyperelastic materials and solving the dispersion curves of prestressed waveguide structures. Furthermore, this paper proposes a mode-tracking algorithm based on image sequential alignment that can achieve the multi-mode classification of guided wave dispersion curves and compare the changes in propagation characteristics of different guided wave modes. The results reveal that the change in guided wave phase velocity produced by prestressing is related to the applied stress, frequency-thickness product, and propagation direction and that the susceptibility of different guided wave modes to prestress varies. Finally, the model approach is validated by comparing its predictions to theoretical results from the literature, which match remarkably well. This study is an important guideline for the preferential selection of environmentally insensitive guided wave modes and excitation frequencies, correction of detection signals, and accurate assessment of engineering structure damage information in ultrasonic guided wave technology engineering applications.