Heritage buildings, worldwide, are marked by the presence of masonry structural elements often affected by shape irregularities if compared with their initial condition. The trigger factors of such geometrical uncertainties can be ascribed to the over centuries deformation processes, to environmental factors or upstream to the constructive methods. The aim of the present paper is the evaluation of the influence of shape irregularities on the collapse condition of circular masonry arches in presence of horizontal seismic actions. In order to take into account a more reliable estimation of the arches bearing capacity a random generative model is developed considering shape uncertainties. A limit analysis based procedure, referring to Heyman’s theory, is used in order to evaluate the horizontal loads multiplier. Then the collapse condition is studied through a probabilistic approach, by analysing the statistical moments up to second order of the results obtained by a Monte Carlo simulation.