Throughout recent history, well documented records of building failures may be found, unfortunately accompanied by great human loss and major economic consequences. One of the mechanisms of failure is referred to as "progressive collapse": one or several structural members suddenly fail, whatever the cause (accident or attack). The building then collapses progressively, every load redistribution in turn causing the failure of other structural elements, until the complete failure of the building or of a major part of it. Various procedures are proposed in the literature in order to simulate the effects of this phenomenon, all of them based on different specific assumptions, such as the independence of the procedure with respect to the cause of the initial failure, or the sequence in which the loads are applied. Since the degree of approximation induced by these assumptions is not discussed in these contributions, the aim of this paper is to assess it. A more complete yet still simplified approach, avoiding some of these assumptions, is devised, based on a finite-element large displacement code, using plastic hinges associated with beam finite elements. Comparisons are established between these results and those obtained with four quasi-static procedures already present in the literature. A discussion based on the results of a large-scale example, provides an assessment of their degree of validity. Discrepancies appear in some cases between the results obtained with the procedures taken form the literature and the reference solutions obtained with the more complete approach. As a result, the better procedures Out of those studied can thus be singled out.