The paper investigates how the deviation of the centreline from the semi-circle influences the mechanical behaviour of gothic masonry vaults. The geometry of the vaults is quantified by a scalar parameter. The present work deals with the force-transmitting system, crack opening magnitude and pattern. Furthermore, the magnitude of the so-called threshold support displacement and the magnitude of the support displacement at first failure is also analysed. Masonry structures consist of separate blocks, each of which can move independently from each other, which makes the calculation process rather complicated. The Discrete Element Method (henceforth DEM) is used to solve the highly nonlinear problem. In the chosen method the equations of motion are solved by the central difference scheme. Approximate boundary conditions are applied, which assume symmetry in the analysed structures. The main findings of the work are: barrel vaults with pointed shape become statically determinate at a higher support displacement level than barrel vaults with semi-circular centreline. In the case of large deviation from the semi-circle or at large support displacement level shear failures can appear in gothic masonry barrel and cross vaults, which could decrease the magnitude of feasible horizontal support displacement.