The　arch　shape　is　a　timeless　structural　solution　as　it　has　been　widely　used　in　the　past　but　is　still　a　common　solution　adopted　nowadays　for　large　spans.　Structural　efficiency　depends　primarily　on　optimal　material　exploitation,　which　allows　us　to　minimize　the　structural　volume.　The　paper　is　framed　in　the　context　of　optimization　of　arch　structures,　and　analytical　design　criteria　are　proposed,　dealing　with　a　specific　class　of　deck　bridges　supported　in　the　mid-span　by　arches.　The　investigation　deals　with　a　simplified　structural　scheme,　constituted　by　statically　determinate　plane　arches　under　self-weight　and　a　single　vertical　load　in　the　key　section,　exerted　by　the　deck　supports.　The　optimization　criterion　assumes　a　constant　normal　stress　in　all　arch　sections　and　the　resulting　arch　shape　is　computed　in　closed　form.　Finally,　the　existence　condition　for　the　proposed　solution　is　provided　and　some　numerical　examples　are　introduced.　©　2018,　Springer-Verlag　GmbH　Austria,　part　of　Springer　Nature.