We illustrate the assumptions underlying a recent reformulation of the thrust network analysis (TNA), a methodology that allows one to model internal forces within masonry arches and vaults by means of a network of thrusts/the proposed version of the TNA allows for analysis of structures of complex geometry, with openings or free edges, subjected to the combined action of vertical and horizontal loadings. Several numerical examples are reported to show how the method can be applied to evaluate the limit geometric proportions, e.g., minimum thickness, or the horizontal load bearing capacity of masonry arches and vaults.