A probabilistic approach to quantifying uncertainties in the progression of severe reactor accidents is formulated and applied to the Source Term Code Package. It is shown that Quantification of uncertainties at the basic level of input parameters reveals broad time-dependent uncertainties in the core melt progression, containment challenges, and fission product releases. Dominant contributors to the source term uncertainties include the core meltdown parameters, the release rate coefficients of fission products, the chemical activity coefficients during core/concrete interactions, and containment performance.