Unstable behavior of boiling water reactors (BWRs) is known to occur during operation at certain power and flow conditions. This paper reports on an uncertainty study of the impact of various parameters on the prediction of the stability of the BWR within the framework of the Organisation for Economic Co-operation and Development Ringhals Unit 1 (Ringhals-1) Stability Benchmark. The time domain code TRACE/PARCS was used in the analysis. The paper is divided into two parts: a sensitivity study on numerical parameters (nodalization, time step, etc.) and an uncertainty analysis of the stability event. The sensitivity study was based on a space-time converged solution, and the most important neutronic and thermal-hydraulic parameters were identified for parameterization. The uncertainty calculation was then performed using the well-established propagation of input errors methodology. Finally, the Spearman Rank method was used to identify the most influential parameters affecting the stability of Ringhals-1.