It is our aim to present a new treatment for some classical models of arches and for their optimization. In particular, our approach allows us to study nonsmooth arches, while the standard assumptions from the literature require W-3,W-infinity-regularity for the parametric representation. Moreover, by a duality-type argument, the deformation of the arches may be explicitly expressed by integral formulas. As examples for the shape optimization problems under study, we mention the design of the middle curve of a clamped arch such that, under a prescribed load, the obtained deflection satisfies certain desired properties. In all cases, no smoothness is required for the design parameters.