A method is presented for the quantitative, model-based safety analysis of nonlinear continuous-time hybrid systems. This method uses the region-transition-model (RTM) framework of [Huang, H., Adjiman, C. S., & Shah, N. (2002). Quantitative framework for reliable safety analysis. AlChE Journal, 48, 78-96], together with a recently developed technique [Lin, Y., & Stadtherr, M.A. (2007). Validated solutions of initial value problems for parametric ODEs. Applied Numerical Mathematics, 57, 1145-1162] for the rigorous global analysis of nonlinear, continuous-time systems with uncertain initial conditions and/or parameters. Given an operating region described by bounds on possible initial conditions, inputs and model parameters, and a finite time horizon, the method can determine which operating subregions lead to safe operation. Numerical examples are presented that demonstrate the effectiveness of the method. This approach can supplement and complement the more qualitative techniques that are widely used for hazard identification and safety analysis. (C) 2008 Elsevier Ltd. All rights reserved.