The building of such a masonry dome posed many technical problems. Though Brunelleschi drew his inspiration from the great dome of the Pantheon in Rome, the formula for its concrete had long since been forgotten. A wooden form had held the Pantheon dome aloft while its concrete set, but for the height and breadth of Neri's dome, starting 52 metres (170 ft) above the floor and spanning 44 metres (144 ft), there was not enough timber in Tuscany to build the scaffolding and forms. Brunelleschi would have to build the dome out of bricks, and with nothing under it during construction. To illustrate his proposed structural plan, he constructed a wooden and brick model with the help of Donatello and Nanni di Banco (on display in the Museo dell'Opera del Duomo). Brunelleschi won by a nose. His model served as a guide for the craftsmen, but was intentionally incomplete, as to ensure his control over the construction.
Brunelleschi's solutions were ingenious. The spreading problem was solved by a set of four internal horizontal stone and iron chains, serving as barrel hoops, embedded within the inner dome: one each at the top and bottom, with the remaining two evenly spaced between them. A fifth chain, made of wood, was placed between the first and second of the stone chains. Since the dome was octagonal rather than round, a simple chain, squeezing the dome like a barrel hoop, would have put all its pressure on the eight corners of the dome. The chains needed to be rigid octagons, stiff enough to hold their shape, so as not to deform the dome as they held it together.
Each of Brunelleschi's stone chains was built like an octagonal railroad track with parallel rails and cross ties, all made of sandstone beams 43 centimetres (17 in) in diameter and no more than 2.3 metres (7.5 ft) long. The rails were connected end-to-end with lead-glazed iron splices. The cross ties and rails were notched together and then covered with the bricks and mortar of the inner dome. The cross ties of the bottom chain can be seen protruding from the drum at the base of the dome. The others are hidden. Each stone chain was supposed to be reinforced with a standard iron chain made of interlocking links, but a magnetic survey conducted in the 1970s failed to detect any evidence of iron chains, which if they exist are deeply embedded in the thick masonry walls.