Since the collapse of the Ronan Point apartment, extensive efforts have been devoted to developing numerical models for assessing the vulnerability of buildings against progressive collapse. The existing numerical models are largely deterministic, where the uncertainties in structural behavior are not considered. This study presents a stochastic numerical model of progressive collapse of reinforced concrete (RC) buildings. In the proposed model, each structural component, such as beam, column, beam-column joint, wall, etc., is modeled as several elastic or rigid blocks connected by nonlinear cohesive elements, which represent the potential damage zones. The constitutive relation of the cohesive element is calibrated by the detailed finite element simulations of the potential damage zone. An Incremental Latin Hypercube Sampling method is further incorporated into the numerical model to perform stochastic simulations of progressive collapse of RC buildings under different column removal scenarios (i.e. different number of columns removed at different locations), in which the fracture energies of the macro-scale cohesive elements are randomized. A family of fragility curves for various possible collapse patterns is generated, which represents a reliability-based measure of the vulnerability of buildings against progressive collapse.