Resin Transfer Molding (RTM) offers the potential to manufacture reinforced thermosetting composites of complex geometries cost-effectively, and at high throughputs. Strong uncertainties inherent in the process, however, stymie robust production of quality composites via this route. Although a number of numerical models have been developed over the years to describe the process, a thorough and systematic analysis of the parameter uncertainties has been the subject of little attention, and forms the focus of this study. This paper presents a stochastic model to investigate the effects of process and material parameter uncertainties on the nonisothermal filling process during resin transfer molding. The analysis is performed in terms of four dimensionless parameters that concisely represent the process physics, and provide for a generalized applicability of the study over a wide range of processing configurations. Parametric studies are conducted to identify optimum values of the dimensionless quantities that minimize the fill time, while simultaneously minimizing the output parameter variabilities. The results of the study provide valuable insight towards robust manufacture of composite materials.