The majority of historical masonry structures include arches and vaults, constructed with or without (dry-joint) any mortar. This paper focuses on dry-joint masonry, because it is common all around the world among architectural heritage. Furthermore, even if there was a mortar in the original construction, it typically suffers from deterioration over its lifetime, often causing total loss of mortar in many of the joints. Due to large horizontal thrust that can be produced, depending on their geometry, arches are typically supported by heavy buttresses. These structures tend to be difficult to model due to their nonlinear nature and inherent discontinuity, which makes it challenging to evaluate their stability. In that context, it is necessary to have realistic numerical models to better diagnose their structural behaviour in a seismic event and, ultimately, to perform only necessary and beneficial interventions. The main goal of this paper is to assess the seismic performance of various dry-joint arch forms with different masonry pier types (i.e. monolithic and regularly coursed) subjected to incrementally increasing lateral loads proportional to the mass (pushover). To achieve this goal, a parametric study is performed on arch curvature and pier morphology. Moreover, the influence of steel tie-rod reinforcement is also examined on the proposed masonry models. These complex masonry arch systems can be simulated with discrete element modeling (DEM) approach. In this research, a commercial three-dimensional discrete element code, 3DEC, is used; in which masonry units are modeled as distinct blocks with zero tensile strength at their joints. The results reveal that pointed arches provide better seismic resistance than the circular arch form. Furthermore, implemented steel tie-rods yield significant increase in stability for the arch-pier structures, which is quantified on different arch curvatures.