The coefficient of friction (CoF) is a very important factor for designing, operating, and maintaining the wheel-rail system. In the real world, accurate estimation of the CoF at the wheel-rail interface is difficult due to the effects of various uncertain parameters, e.g., wheel and rail materials, rail roughness, contact patch size, and so on. In this study, a stochastic analysis using polynomial chaos (poly-chaos) theory is performed with the newly developed 3D dry CoF model at the wheel-rail contact. The wheel-rail system is modeled as a mass-spring-damper system. Stochastic analyses with one uncertainty, combinations of two uncertainties, and a combination of three uncertainties are performed. The probability density function (PDF) results for stick CoF, slip CoF, and combined (total) CoF are presented. The stochastic analysis results show that the total CoF PDF before 1 s is dominantly affected by the stick phenomenon, whereas the slip dominantly influences the total CoF PDF after 1 s. The CoF PDFs obtained from simulations with combinations of two and three uncertain parameters have wider PDF ranges than those obtained for only one uncertain parameter. The current work demonstrates that the CoF is strongly affected by the stochastic variation of dynamic parameters. Thus, the PDF distribution of the CoF could play a very important role in the design of the wheel-rail system.