A simple suspension bridge (also rope bridge, swing bridge (in New Zealand), suspended bridge, hanging bridge and catenary bridge) is a primitive type of bridge in which the deck of the bridge lies on two parallel load-bearing cables that are anchored at either end. They have no towers or piers. The cables follow a shallow downward catenary arc which moves in response to dynamic loads on the bridge deck.

The arc of the deck and its large movement under load make such bridges unsuitable for vehicular traffic. Simple suspension bridges are restricted in their use to foot traffic. For safety, they are built with stout handrail cables, supported on short piers at each end, and running parallel to the load-bearing cables. Sometime these may be the primary load-bearing element, with the deck suspended below. Simple suspension bridges are considered the most efficient and sustainable design in rural regions, especially for river crossings that lie in non-floodplain topography such as gorges.

In some contexts the term "simple suspension bridge" refers not to this type of bridge but rather to a suspended-deck bridge that is "simple" in that its deck is not stiffened. Although simple suspension bridges and "simple" suspended deck bridges are similar in many respects, they differ in their physics. On a simple suspension bridge, the main cables (or chains) follow a hyperbolic curve, the catenary. This is because the main cables are free hanging. In contrast, on a suspended deck bridge (whether "simple" or not) the main cables follow a parabolic curve. This is because the main cables are tied at uniform intervals to the bridge deck below (see suspension bridge curve).

The differences between these two curves were a question of importance in the 17th century, worked on by Isaac Newton. The solution was found in 1691, by Gottfried Leibniz, Christiaan Huygens, and Johann Bernoulli who derived the equation in response to a challenge by Jakob Bernoulli. Their solutions were published in the Acta Eruditorum for June 1691.

A stressed ribbon bridge also has one or more catenary curves and a deck laid on the main cables. Unlike a simple suspension bridge however, a stressed ribbon bridge has a stiff deck, usually due to the addition of compression elements (concrete slabs) laid over the main cables. This stiffness allows the bridge to be much heavier, wider, and more stable.

The simple suspension bridge is the oldest known type of suspension bridge and, ignoring the possibility of pre-Columbian trans-oceanic contact, there were at least two independent inventions of the simple suspension bridge, in the wider Himalaya and East Asian region and in South America.

The earliest reference to suspension bridges appear in Han dynasty records on the travels of Chinese diplomatic missions to the countries on the western and southern fringe of the Himalaya, namely the Hindukush range in Afghanistan, and the lands of Gandhara and Gilgit. These were simple suspension bridges of three or more cables made from vines, where people walked directly on the ropes to cross. Later, they also used decking made from planks resting on two cables.

In South America, Inca rope bridges predate the arrival of the Spanish in the Andes in the 16th century. The oldest known suspension bridge, reported from ruins,^{[clarification needed]} dates from the 7th century in Central America (see Maya Bridge at Yaxchilan).