To address the stability degradation problem in Series-Series (S-S) Wireless Power Transfer (WPT) systems caused by parameter uncertainties, this paper employs a Global Sensitivity Analysis (GSA) based on the Sobol’ method to determine the influence of each parameter on system stability. Firstly, a Generalized State-Space Averaged (GSSA) model that reflects the system’s dynamic characteristics is established. Based on this model, the Sobol’ GSA method is applied to quantitatively analyze the impact of key parameters and their interactions on system stability, using the real part of the dominant eigenvalue as the stability metric. The analysis results reveal that the load resistance is the most dominant factor in terms of independent influence on system stability. However, it is further demonstrated that the overall system stability is governed by strong nonlinear interactions among all parameters. Notably, parameters often overlooked in traditional analysis, such as primary and secondary self-inductances, also exhibit significant total-effect sensitivity.