To quantify the safety of masonry arches and vaults using limit-analysis, various types of safety factors have been devised. The most well-known were introduced by Heyman: a “static factor of safety” (or load factor) assessing how vulnerable the structure is to increases in the living loads and a “geometrical factor of safety” assessing how critical the thickness of the structure is for its stability. In non seismic areas, one of the main risks of total or partial collapse of arches and vaults is excessive displacement of the supports (following walls or soil deformation). Limit analysis technique can be used to analyse this risk, quantifying movements permitted before collapse and evolution of the thrust on the supports. This analysis can be combined with pathological investigations and displacement monitoring to study the evolution of the risk and define a “kinematic factor of safety”. A software program was developed (a) to compute domains of stability for particular mechanisms of deformation, (b) to study possibility of transitions between mechanisms during deformation and (c) to interactively study the influence of movements of the supports on thrust and stability. Scaled physical models are used to validate the limit analysis approach, using an experimental rig where horizontal and vertical displacements are controlled by computer. A high-speed camera is used to study transition between mechanisms. Finally it is referred to techniques integrating this kinematic approach into a more general probabilistic approach, taking into account various uncertainties in the structure (shape, thickness, loads, movements).