In this study, an enhanced non-isothermal, two-phase 1D analytical proton exchange membrane fuel cell (PEMFC) model is developed, which not only considers the water saturation jump, but also proposes a novel method to analytically solve the water phase changes and couple the liquid and vapor transport together. A stringent model validation procedure is used to show good agreement between the simulated results and the experimental data, taking advantage of the "three-step" and "multi-case" validation methods. It is revealed that the uncertain parameters may deteriorate model reliability and credibility, thus demonstrating the necessity to conduct sensitivity analysis. A multi-parametric screening method i.e. the elementary effect (EE) method based on Monte Carlo experiments is implemented to comprehensively analyze the total 22 uncertain parameters (including geometric, physical and electrochemical parameters), which are finally classified into very sensitive ones, rather sensitive ones and insensitive ones. The cathodic parameters are found more sensitive than the anodic ones, and the parameters of different components may have distinct sensitivity. Besides, whether the effect of each parameter is positive or negative on cell performance is also discussed. Furthermore, three cases with different groups of parameters are presented, which show almost the same polarization curve, and the two sample Kolmogorov-Smirnov (KS) test is applied to verify the stability difference. It is concluded that those uncertain parameters not only influence the cell performance but also affect the model stability, and hence the effects of varying operating conditions should be taken into account in validation work.