•The collapse condition of the masonry arch on spreading support is investigated.•An incremental numerical procedure is developed in finite displacement field.•Geometrical uncertainties of the masonry arch are described by random variables.•Masonry arch with irregularities has lower displacement capacity than nominal arch.•The results obtained by numerical analyses are in agreement with experimental tests. This work is aimed at evaluating the collapse displacement of masonry arch subjected to spreading supports. This is achieved through a general application of the virtual works principle. The problem is described in a finite displacements formulation and investigated with a probabilistic approach, also considering the effects of the geometrical uncertainties. This aspect is related to the imperfections of the voussoirs, which affect the structural shape. The comparison between the numerical and experimental results, derived both by the literature and laboratory tests, confirms that the geometrical irregularities can significantly affect the results obtained on the nominal structural geometry. Moreover, the disagreement observed in the experimental tests is explained.