The effect of shear sliding on the failure load and collapse mode of segmental arches is studied with a Non-Smooth Contact Dynamics (NSCD) approach, which allows a full 3D dynamic analysis of complex systems of rigid blocks in frictional contact à la Coulomb. The numerical solution at each time-step relies upon an associative frictional model, but a successive ad hoc stabilization procedure annihilates the dilatation effects so that, in practice, the frictional model evolves into non-associative friction. Within static analyses, we proceed from voussoir arches to multi-ring arches, either isolated or inserted in walls; we decompose the contributions of the various mechanisms (rotation and sliding) which act within the bond pattern, plotting the effective thrust line calculated with the NSCD approach. Concerning dynamic analyses, we depict the sliding forces overcoming the frictional forces between blocks in paradigmatic examples. The numerical simulations not only indicate the failure load, but also illustrate the interactions between moment and shear at failure, thus providing the necessary information for possible consolidation strategies.